Medvedev entered this week knowing victory at the Mexican Open would see him move to the top of the ATP rankings for the first time.
But the Russian was still waiting to play his quarter-final on Thursday when his ascension was confirmed courtesy of Djokovic's last-eight defeat in Dubai.
Djokovic, a seven-time year-end number one, had led the rankings for 86 consecutive weeks, boosting his record total to 361 weeks.
In his first tournament since missing the Australian Open, however, the five-time Dubai champion struggled to match 123rd-ranked Vesely and went down 6-4 7-6 (7-4).
Djokovic might have known what to expect, having lost his only prior meeting with Vesely in Monte Carlo in 2016.
The Serbian looked like getting to grips with his opponent at the start of the second set, applying pressure, but was then broken again and had to respond strongly to reach a tie-break.
Again, Vesely led, and Djokovic's match was summed up by a double-fault immediately after winning back the mini-break, allowing the Czech to prevail.
The victor hailed the end of Djokovic's reign, saying in his on-court interview: "It's great for tennis to have somebody new as world number one again.
"We all know Novak missed the Australian Open, but he's been such a champion, as world number one for 361 weeks.
"Tennis needs new number ones, new generations coming up, so I think it's just great."
As Vesely advances, second seed Andrey Rublev will fancy his chances of a second straight ATP Tour title after his win at the Open 13 Provence.
Rublev stretched his winning streak to seven matches in coming from behind to beat Mackenzie McDonald and make the semi-finals, where he will play Hubert Hurkacz, who defeated Jannik Sinner.
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.
The 33-year-old, who triumphed in Montpellier in 2010 and 2014, won 7-5 6-3 to become the eighth French champion in the 10 editions of the tournament since it was relocated from Lyon.
Pospisil, who battled past second seed David Goffin to reach only his second ATP Tour final, failed to make the most of four break points against the Monfils serve in an hour and 37 minutes.
At the Pune Open, Jiri Vesely ended a five-year wait to lift a Tour title after overcoming Egor Gerasimov.
Vesely saved match points in his quarter-final and semi-final to book a showdown with Gerasimov, which he won 7-6 (7-2) 5-7 6-3.
"I have to be realistic. I had a lot of luck in the week, saving six match points [across] two matches in a row," he said.
"I think that happens once in a lifetime, maybe, you never know…
"Two matches in a row, especially in the quarter-finals and semi-finals, is really big."
Vesely is the eighth player since 2013 to save match points in two matches en route to winning a Tour event.
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.
Having made headlines after his semi-final triumph over Hubert Hurkacz by writing "no war please" on a television camera in protest at Russia's invasion of Ukraine, Rublev wrapped up his third title in just a matter of days in emphatic fashion, after winning both the singles and doubles titles at the Open 13 Provence in Marseille last week.
The Russian world number seven had needed three sets in each of his last three contests but wrapped up a more straightforward victory against his Czech opponent, who had defeated 20-time Grand Slam champion Novak Djokovic en route to the final.
Rublev broke Vesely's serve in the fourth game of the contest, not dropping a single point behind his first serve as he roared to a 6-3 win in the opening set.
The 24-year-old then broke again in the opening game of the second set, before the Czech, ranked number 123 in the world, battled back bravely to level the set at 3-3.
Rublev responded in brutal fashion, however, immediately breaking again and going on to seal a comfortable victory, hitting just eight unforced errors throughout the contest, as he claimed his 10th career title.
The victory made it 13 match wins in a row for Rublev across singles and doubles after his successful time in Marseille, where he successfully teamed up with Ukrainian Denys Molchanov for a symbolic doubles triumph.
"I was lucky today, and that's why I am happy to be the champion, I didn't expect this," said Rublev. "It's an amazing feeling and I don't know what to say."
Verdasco, the ninth seed at the ATP 500 tournament, was beaten 6-3 6-3 by fellow Spaniard Pablo Andujar on the clay in Brazil.
The 36-year-old has fallen to three straight losses, the first of which was a third-round defeat at the Australian Open.
Verdasco – the 2018 runner-up – was one of three seeds tested, but Garin survived a test against Andrej Martin.
Garin, who won the title in Cordoba earlier this month, needed more than three hours to edge Martin 4-6 7-5 7-6 (7-5).
Albert Ramos-Vinolas departed, the seventh seed falling to 16-year-old Carlos Alcaraz 7-6 (7-2) 4-6 7-6 (7-2) after three hours, 36 minutes.
Federico Delbonis advanced, while wildcard Thiago Seyboth Wild needed almost four hours to get past Alejandro Davidovich Fokina 5-7 7-6 (7-3) 7-5.
There were also upsets at the Delray Beach Open, where John Millman and Adrian Mannarino were beaten in the first round.
Millman, the fifth seed, went down to Yoshihito Nishioka 3-6 6-4 6-2 and seventh seed Mannarino fell to Kwon Soon-woo 1-6 6-3 6-2.
Frances Tiafoe, the champion in 2018, came through his opener against qualifier Emilio Gomez.
