Despite breaking Dzumhur's serve at the first opportunity, Auger-Aliassime – who failed to get past the first round of the Australian Open – conspired to lose the first set, as his counterpart broke back straight away and eventually closed out the set in the tie-break.
That seemed to be the shot in the arm Auger-Aliassime needed, as the Canadian world number 21 cruised through the second and third sets – enjoying three breaks of service in the latter, though it still took him two hours, 31 minutes to clinch Tuesday's win.
Victory sets up a second-round clash with France's Pierre-Hugues Herbert, who eliminated Sergiy Stakhovsky 6-2 7-5, while seventh seed Filip Krajinovic also went through in straight sets, beating Enzo Couacaud 6-4 6-4.
Kazakhstan's Alexander Bublik will face second seed David Goffin next after a gruelling 6-7 (7-2) 6-1 7-6 (7-2) win over Henri Laaksonen.
Mikael Ymer and Emil Ruusuvuori also secured passage to the last 16.
James Duckworth was the highest seed in action at the Pune Open on Tuesday and the Australian – who is the sixth favourite – had little difficulty getting past Peter Gojowczyk 7-6 (7-5) 6-4.
The home contingent had mixed success. Arjun Kadhe lost out 6-2 6-4 to Jiri Vesely, but Prajnesh Gunneswaran ousted Yannick Maden 7-6 (7-4) 7-6 (7-5) to progress.
Ilya Ivashka, Nikola Milojevic, Egor Gerasimov and Roberto Marcora all made it through as well, the latter set to face top seed Benoit Paire next.
Following his success over De Minaur at the Moselle Open last week, Giron beat the world number 26 once more as he battled to a 7-6 (7-5) 7-6 (7-2) victory in two hours.
The unseeded American, appearing for the first time in Sofia, rallied from a break down in the second set to reach an ATP Tour quarter-final - where he will meet John Millman - for the fourth time this season.
Millman, who is seeded eighth, lost the first set against qualifier Illya Marchenko but recovered well to comfortably triumph 5-7 7-6 (7-0) 6-3.
However, it was far more straightforward for the other favourites, with top seed Jannik Sinner avoiding a second-set blip to defeat Egor Gerasimov 6-2 7-6 (7-3) and Gael Monfils getting a walkover against Ilya Ivashka.
Number five seed Filip Krajinovic coasted past fellow Serbian Laslo Djere 6-3 6-0 in just over an hour to set up a quarter-final tie with Kamil Majchrzak.
In Thursday's other match, world number 56 James Duckworth smashed Benoit Paire 6-4 6-4 in just an hour and 15 minutes to collect his 11th win in his past 12 outings.
Duckworth, who reached his first ATP Tour final in Nur-Sultan last week, will now challenge defending champion Sinner in the next round.
The world number one is competing in his first tournament since his dream of winning a calendar Grand Slam was ended by Daniil Medvedev in September's US Open final.
After beating Marton Fucsovics in three sets and then benefiting from a walkover against Gael Monfils in the last 16, Djokovic made light work of Fritz in Friday's quarter-final.
He sent down eight aces and was successful with 72 per cent of his first serves that landed on his way to a 6-4 6-3 victory.
However, Djokovic lost his serve on three occasions and, while happy with his overall display, the Serbian feels like there is more to come from his game in the French capital.
"I was absent from the tour for two months coming into this tournament," he said. "The last competitive match I played was in the US Open final, compared to the other guys playing one or two events prior to Paris.
"I knew that I needed to start well, with good intensity and put in a lot of hours on the practice court. But it's different when you play points in a competitive match.
"I am pleased with the way I played against Fucsovics and again today, though I did have ups and downs. I am not entirely pleased with the way I closed out the sets.
"I backed myself up with good returns and read Taylor's serve very well to get into rallies. I closed out the last couple of service games well and that's a positive."
Djokovic is aiming to win the Paris Masters for a record-extending sixth time in his bid to end the year as world number one for a record seventh occasion.
The Serbian will contest his 71st career Masters 1000 semi-final – four short of Rafael Nadal's record – against Hubert Hurkacz, who saw off James Duckworth 6-2 6-7 (4-7) 7-5.
With that victory, the world number 10 clinched the final singles spot at the ATP Finals in Turin later this month.
Hurkacz is the second Polish player to qualify for the event after Wojtek Fibak in 1976. It also means only European players will feature in the ATP and WTA Finals for the first time ever.
Saturday's other semi-final in Paris will be contested between Djokovic's US Open conqueror Medvedev and Olympic gold medallist Alexander Zverev.
Home favourite Hugo Gaston eliminated Pablo Carreno Busta earlier in the tournament but was always likely to face a tougher task against Medvedev.
So it proved, with the qualifier going down 7-6 (9-7) 6-4 in a match that saw Medvedev hit 13 aces to his opponent's one.
"When the atmosphere is against you, you need to face it," Medvedev said. "You need to try to win, no matter what.
"Even when it is against me, I think, 'I will try to beat my opponent and the crowd' because there is no other choice."
Zverev kept his momentum going with a 7-5 6-4 win over Casper Ruud in Friday's final contest, as he made it eight wins on the bounce.
The German held serve throughout, while breaking his opponent twice, to remain on course for a sixth final of 2021.
Duckworth sent down 14 aces, winning 85 per cent on his first serve, and hit 53 winners as he got past Popyrin 7-5 4-6 6-1 in two hours and 20 minutes.
Popyrin could only manage 35 winners with 18 unforced errors. Duckworth will face one of the American qualifiers, Mitchell Krueger and Christopher Eubanks in the next round.
Wolf needed one hour and 52 minutes to topple countryman Kozlov 6-2 7-6 (8-6), converting three of his six break points, getting the edge by winning 50 per cent on Kozlov's second serve.
In the battle of the Argentines, Tomas Martin Etcheverry defeated Facundo Mena 7-6 (8-6) 6-3. Mena hit 28 winners but was undone by 23 unforced errors.
Frenchman Constant Lestienne fought back from a set down to win over American wild card Brandon Holt 5-7 7-6 (7-5) 6-3.
Top seed Hurkacz defeated German qualifier Peter Gojowczyk 6-4 7-6 (7-4) to stand on the brink of a third title of the year.
The world number 13 from Poland won 79 per cent of the points on his first serve and sealed victory in an hour and 37 minutes.
Gojowczyk saved five break points but was unable to pull off an upset in Metz.
Hurkacz said: "Peter played a really great match. He was super tough to play against, so I am proud of myself that I managed my emotions and played a good tie-breaker.
"I was trying to keep holding serve to stay in the second set and ended up taking the set in the tie-breaker."
Carreno Busta ended Gael Monfils' bid to win the title on home soil, the Spaniard triumphing 7-5 7-6 (10-8).
Monfils was 5-3 up in a second-set tie-break but failed to force a decider as Carreno Busta advanced for a showdown with Hurkacz.
James Duckworth is into his first ATP Tour final after beating eighth seed Ilya Ivashka 6-3 7-6 (7-4) at the Astana Open.
The Australian will face Kwon Soon-woo, who upset second seed Alexander Bublik 3-6 7-5 6-3.
The South Korean came out on top in the battle of the unseeded first-time finalists on Sunday, winning 7-6 (8-6) 6-3 in Nur-Sultan.
Kwon won 86 per cent of points behind his first serve and came from behind in both sets to be crowned champion.
Australian Duckworth failed to convert three set points in a tie-break and Kwon made him pay, grasping his first opportunity to go a set up.
Kwon was broken in the first game of the second set, but the battling world number 82 hit straight back to draw level.
Duckworth, who had not dropped a set en route to the final, was broken again to trail 4-2 and he was unable to find a way back as the 23-year-old Kwon celebrated his finest hour.
The seventh-seeded Frenchman, knocked out by Aljaz Bedene in the first round at Roland Garros, was beaten 6-3 6-2 by a player ranked 65 places lower than him, with Duckworth outside the world's top 100.
Home hopes Yannick Hanfmann and Peter Gojowczyk progressed, the latter coming from a set down to beat Ilya Ivashka 5-7 6-4 6-2, but there was no such joy for fellow German Dominik Koepfer after he fell to wildcard Jurij Rodionov.
Elsewhere in the draw, there were wins for Feliciano Lopez, Sam Querrey, Dominic Stephan Stricker and Jordan Thompson.
The world number nine downed Slovakian Gombos 6-3 6-4 in Montpellier on Friday to stay in contention to win the tournament for a third time.
Filip Krajinovic stands in the way of Monfils and a place in the final after the seventh seed accounted for Gregoire Barrere 6-2 7-5.
Vasek Pospisil moved into the last four when Richard Gasquet retired at 6-1 1-0 down in his homeland due to an abdominal injury.
David Goffin will take on the Canadian after the second seed saw off Pierre-Hugues Herbert 6-4 7-6 (7-5).
James Duckworth reached his maiden ATP Tour semi-final with a 6-3 7-6 (7-4) defeat of qualifier Roberto Marcora at the Pune Open.
The 96-ranked Australia will come up against Egor Gerasimov, who came from a set down to beat Kwon Soon-woo 4-6 7-6 (7-1) 6-4.
Jiri Vesely and Ricardas Berankis will contest the other semi-final after getting past Ilya Ivashka and Yuichi Sugita respectively.
Seeking his third title at the event, world number nine Monfils triumphed 7-6 (7-4) 6-2 in 82 minutes against the Serbian.
Monfils saved all three break points against Krajinovic in an impressive victory that maintains France's perfect record of ensuring a home player reaches the final of the Montpellier tournament.
The 2010 and 2014 champion will meet Pospisil on Sunday after the Canadian defeated David Goffin in three sets.
Goffin served for the match in the decider but lost three decisive games in a row as Pospisil triumphed 6-3 1-6 7-5 in two hours and 21 minutes.
At the Pune Open, Australia's James Duckworth was beaten 7-6 (7-2) 6-4 by Egor Gerasimov in the semi-finals.
The Belarusian dropped only five points behind his first serve as he reached a maiden ATP Tour final, where he will face Jiri Vesely.
Vesely saved match points for the second round in a row, outlasting second seed Ricardas Berankis 6-7 (8-10) 7-6 (7-3) 7-6 (9-7) in a draining encounter to secure a first final in nearly five years.
Murray needed less than an hour to record a 6-2 6-0 triumph over the big-serving American, setting up a last-16 meeting with Australia's Max Purcell.
Three-time grand slam champion Murray hobbled out of his last meeting with Querrey at the Wimbledon quarter-finals in 2017, a defeat which marked the start of his injury woes.
But he produced a polished display on the grass to wrap up his eighth career win over the American on Tuesday.
Elsewhere in Rhode Island, eighth seed James Duckworth battled to a 6-2 4-6 6-2 win over Liam Broady, and seventh seed Jiri Vesely raced to a 6-4 6-2 triumph against Spain's Feliciano Lopez.
Meanwhile, Thiem ended a 426-day wait for a Tour-level win by overcoming Finland's Emil Ruusuvuori 3-6 6-1 7-6 (7-5) at the Swedish Open.
The Austrian, who has won 17 career titles, halted a run of 10 consecutive losses on the ATP Tour with his first triumph since he beat Marton Fucsovics at the last-32 stage of the Internazionali d'Italia in May 2021.
The 28-year-old expressed his delight at ending his drought in the aftermath, saying: "It's a long time. My last victory was in Rome in 2021, it feels like a different world somehow.
"Many, many things happened. It was tough, but it was also a very good experience I think, for life in general. I'm so happy that I got this first victory here today."
Thiem will face fourth seed Roberto Bautista Agut in the last 16, while Sebastien Baez will take on Alejandro Davidovich Fokina after the former beat Fabio Fognini in straight sets.
The round of 32 did see two shock exits, however, with seventh seed Holger Rune succumbing to a 6-3 6-3 defeat against Switzerland's Marc-Andrea Huesler, and Nikoloz Basilashvili being forced to retire at one set down against Hugo Gaston.
Also, Francisco Cerundolo beat Pedro Sousa to set up an enticing clash with top seed Casper Ruud.
Ruud, a French Open finalist and defending champion in Bastad , lacked his usual composure as world number 39 Cerundolo broke him three times to win 6-4 3-6 7-5 on Wednesday.
That marked a first top-10 career victory for Cerundolo after defeating world number five Ruud, guiding him to his first quarter-final appearance at the tournament.
"I'm feeling amazing, I'm really happy," said Cerundolo, whose previous best result was beating world number 24 Gael Monfils. "It's amazing getting my first Top 10 win. It's been the best year so far in my career.
"He's a French Open finalist and was the defending champion here, so it was a big challenge for me and I'm happy to go through."
Aslan Karatsev awaits in the quarter-finals Cerundolo after downing Frenchman Hugo Gaston 6-2 6-4.
Fifth seed Pablo Carreno Busta survived a first-set scare to defeat 2016 champion Albert Ramos-Vinolas 4-6 7-6 (7-5) 7-5.
The victory was Carreno Busta's 250th tour-level triumph and he will next face third favourite Diego Schwartzman, who overcame Elias Ymer in straight sets.
Third seed Alexander Bublik was made to work for a 6-3 3-6 6-2 second-round victory over Jack Sock in Newport and Andy Murray edged past Wimbledon doubles champion Max Purcell.
Murray needed almost two-and-a-half hours to get the better of Purcell, eventually triumphing 4-6 6-2 6-1 to tee up a last-eight meeting with Bublik.
Fourth favourite Maxime Cressy had little trouble in beating fellow American Mitchell Krueger 6-3 6-4 and will next face Steve Johnson, who progressed past seventh seed Jiri Vesely with a walkover.
Benjamin Bonzi, ranked as fifth seed in the United States, eased past Christopher Eubanks in straight sets, while James Duckworth triumphed 7-5 3-6 6-2 over Quentin Halys.
John Isner joined the list of favourites who made the third round in routine fashion, beating Peter Gojowczyk in straight sets 6-3 7-6 (8-6), before top seed Felix Auger-Aliassime faced some adversity against Jason Kubler following the Australian's strong run into the fourth round of Wimbledon.
Auger-Aliassime has a slight advantage, leading 6-4 3-6 6-5 before play was suspended due to poor light. When play resumes, Kubler will serve with a chance to force a third-set tiebreak.
French Open quarter-finalist Sinner took just 61 minutes to seal a 6-1 6-2 victory against Duckworth, who replaced Hubert Hurkacz after the Pole withdrew due to food poisoning.
The 19-year-old Italian reached a career high 46 in the rankings following his exploits at Roland Garros and cruised past Duckworth after fending off two break points in a 12-minute game at 2-2 in the second set.
Sinner will go up against qualifier Pierre-Hugues Herbert in round two after the Frenchman defeated Tennys Sandgren 6-3 3-6 6-3 at the ATP event on Tuesday.
Zverev defeated Felix Auger-Aliassime in the final of last week's tournament in Cologne and will begin his bid for a second straight title against Millman after the Australian overcame Fernando Verdasco 6-4 6-2.
At the European Open in Antwerp, Alex De Minaur came from a set down to defeat veteran Richard Gasquet 3-6 7-6 (7-5) 6-3.
When serving for the set in the second set, Gasquet produced an unforced error following a reactive backhand from De Minaur. He then double faulted at 5-5 in the tie-break and the Australian eighth seed dished out the ultimate punishment.
Federico Coria stepped in after Kei Nishikori withdrew due to a right shoulder injury and the Argentinian was comfortably beaten 6-2 6-3 by Pablo Andujar.
The top seed won just two points across the first three games but took a first set that featured four breaks and lasted over an hour.
Duckworth broke in the first game of the second but eventually ceded that advantage and the frustrated Australian could not prevent Sinner from breaking again to claim a 7-6 (7-4) 6-4 win to set up a last-four clash with Filip Krajinovic, who prevailed in three sets against Kamil Majchrzak.
Gael Monfils will feature in the other semi-final after brushing aside Gianluca Mager 6-2 6-2, booking a meeting with American Marcos Giron.
It is a second semi-final in as many weeks for Monfils, who also reached the last four in Metz.
Giron will contest his first Tour-level semi-final following a 6-4 6-2 defeat of John Millman.
"Nothing is easy," Monfils said. "We have been putting in work for nearly four days here. Working on my serve and my forehand and it worked perfectly today. I will be ready for Marcos. He has been playing very well, so I think it will be a tough semi-final."
World number 84 Ruusuvuori saved a set point in the first-set tie-break on his way to a 7-6 (8-6) 6-4 victory and will now face Ilya Ivashka for a place in the semi-finals.
There was nearly another upset as home hopeful Alexander Bublik, seeded second, had to recover from a set down to overcome Miomir Kecmanovic 2-6 6-3 7-5.
Carlos Taberner awaits Bublik in the next round after the Spaniard beat Egor Gerasimov 5-7 7-6(5) 7-5.
Kwon Soon-woo and James Duckworth saw off Dusan Lajovic and Filip Krajinovic respectively in straight sets to remain a course for glory.
At the Moselle Open in Metz, meanwhile, Gael Monfils took out Philipp Kohlschreiber 7-6(2) 6-4 to reach the quarter-finals on home soil.
Tournament favourite Hubert Hurkacz made light work of 2016 champion Lucas Pouille with a 6-2 6-3 victory to set up a meeting with Andy Murray in the quarter-finals.
Elsewhere on Thursday, German qualifier Peter Gojowczyk proved too strong for Karen Khachanov and will now face Marcos Giron, who upset fourth seed Alex de Minaur.
The two-time Wimbledon champion recovered from a set down to win 4-6 6-3 6-2 6-4 against the Australian on Monday.
Murray maintained his record of having never lost in the first round at SW19, throwing in an underarm serve to help him win a point in the third set.
The Scot insisted using the underam serve, a move often associated with Duckworth's compatriot Nick Kyrgios, is a legitimate tactic and not a sign of disrespect to an opponent.
"He changed his return position, that's why I did it," Murray explained after the match.
"He was struggling a little bit on the first-serve return, so he stepped probably two metres further back. As soon as I saw him step further back, I threw the underarm serve in.
"I personally have no issue with players using it. I never have. Certainly more and more players have started returning from further behind the baseline now to give themselves an advantage to return.
"No one says it's disrespectful for someone to return from five or six metres behind the baseline to try to get an advantage.
"So I used it, not to be disrespectful to him, but to say, 'if you're going to step further back to return the serve to give yourself more time, then I'm going to exploit that'.
"I've never understood that [argument it is disrespectful]. It's a legitimate way of serving.
"I would never use an underarm serve if someone was standing on the baseline because I think it's a stupid idea because they're going to track it down and it's easy to get.
"If they stand four or five metres behind the baseline, then why would you not do that to try to bring them forward if they're not comfortable returning there? Tactically, it's a smart play."
Murray will face big-serving American John Isner in the second round on Wednesday, having won each of the duo's eight previous head-to-head meetings.
He was happy with how he felt physically after beating Duckworth, having returned from the abdominal injury he suffered while reaching the Stuttgart Open final earlier this month.
"The last few days when I've been serving was fine," he said. "I went to get an ultrasound scan on it on Saturday after my practice just to see how it was progressing.
"It was all clear for the first time on the scans, which is really positive. I wanted that kind of for my own peace of mind to know that the injury has healed.
"Obviously I still need to take precautions and still do some rehab and protect it when I can, but in the match it was absolutely fine."
Two-time Wimbledon champion Murray took two hours and 43 minutes to record a 4-6 6-3 6-2 6-4 win over the Australian, maintaining his record of having never fallen at the first hurdle in SW19.
Murray is making just his second Wimbledon appearance since 2017 and is looking to better last year's run to the third round, where he suffered a straight-sets reverse against Denis Shapovalov.
Having endured a spate of injuries and undergone two hip surgeries since his last Wimbledon triumph in 2016, the 35-year-old said he will enjoy every opportunity he gets to play in front of a home crowd on Centre Court.
"It's amazing to be back out here again with a full crowd after the last few years, amazing atmosphere," he said.
"Obviously I'm getting on a bit now, so I don't know how many more opportunities I'll get to play on this court. I want to make the most of every time I get to come out here now.
"I'm glad I managed to get through and hopefully I'll get another match on here in a couple of days."
After fighting back to beat the world number 74, Murray expressed his hope he could grow into the tournament as he advances.
"I thought I did well to rebound after the first set, he likes playing on the grass, he's come back from a hip surgery himself in January and was playing very well," he added.
"Once I started to find my returns a little bit more as the match went on, I felt a bit more comfortable and did well to get through.
"Naturally, there's always nerves and pressure and butterflies and stress and all of those things before the first match, it was a longer build-up for me than usual because of the ab injury I had after Stuttgart [where Murray finished as runner-up earlier this month].
"I've done a lot of practising here, I've been at the venue a lot in the last couple of weeks so yeah, it was great to get out here, get a win under my belt and hopefully I'll play better from here on in."
Murray will face big-serving American John Isner in the second round on Wednesday, having won each of the duo's eight previous head-to-head meetings.
