The 31-year-old Argentine, who is currently ranked 41st in the world, went down 6-4 6-2 to the 111th-ranked Spaniard.
Former top 10 player Fernando Verdasco was also beaten on Tuesday, going down to Argentine Sebastian Baez 7-6 (8-6) 7-5.
The 38-year-old Spaniard dropped out of the top 100 last year for the first time since 2004 after a difficult season with a long-term leg injury and COVID-19 prior to the French Open.
Baez will play Chilean third seed Cristian Garin in the second round, while Taberner will meet qualifier Alejandro Tabilo after he beat wild card Francisco Cerundolo 6-4 6-1.
Lucky loser Colombian Daniel Galan also progressed into the last 32 after a 7-5 6-3 victory over Bolivian Hugo Dellien, while sixth seed Albert Ramos-Vinolas triumphed 6-4 6-3 over Andrej Martin.
Kubler and Verdasco endured a 71-minute first-set tussle, which the Australian edged 9-7 in a tie-break before dominating the second frame, dishing out a bagel in 29 minutes to win 7-6 (9-7) 6-0.
World number 71 Kubler progressed to the second round where he will take on Colombia's Daniel Elahi Galan who defeated China's Zhang Zhizhen 6-2 6-3.
Johnson set up a second-round clash with American compatriot and top seed Frances Tiafoe after getting the better of Facundo Bagnis 7-6 (7-5) 1-6 6-1 in one hour and 55 minutes.
USA's Kudla also progressed with a hard-fought 6-4 4-6 6-4 victory over Australia's Aleksandar Vukic in just under two hours.
Dutchman Gijs Brouwer won 6-4 6-4 over Aleksandar Kovacevic, setting up a meeting with big-serving fourth seed John Isner.
Moraing, who is ranked 252 places below Djokovic, beat Egor Gerasimov 4-6 7-6 (9-7) 7-5 in a gruelling encounter on Monday.
Djokovic is seeking his 83rd Tour-level title as he warms up for the French Open, the main draw of which begins on May 30.
Fellow home favourite Dusan Lajovic, the highest seed to compete on day one, will meet Jeremy Chardy next after beating Ricardas Berankis in straight sets.
Eighth seed Federico Delbonis required three sets to see off Lukas Klein, while seventh seed Miomir Kecmanovic – another Serbian in the draw – was beaten 6-3 6-2 by Pablo Cuevas.
Veteran Fernando Verdasco set up a contest with Adrian Mannarino after an impressive 7-5 6-2 win over Lucas Pouille.
At the Emilia-Romagna Open in Parma, all of Monday's play had to be cancelled due to persistent rain.
Fifth seed Richard Gasquet is in action on Tuesday.
A 6-4 6-4 loss came against a player he once led 13-1 in their career head-to-head, a gap which has now closed to 13-4 after a hat-trick of wins for Spanish left-hander Verdasco.
Following victories for Verdasco at the US Open and Shenzhen Open in 2018, the Madrid man again got the better of the two-time Wimbledon champion, beating the Scot on an indoor hard court for the first time after five previous defeats.
It was a tough draw for Murray, who also struck unlucky at the French Open last month when he was paired with former champion Stan Wawrinka in the first round and also lost in straight sets.
The former world number one had entered the Cologne event, a low-level ATP 250 tournament, in the hope of building up match practice and registering the wins he needs to improve his ranking, which stands at 115 after his battle with injury in recent seasons.
Marin Cilic and Gilles Simon won through to the second round earlier in the day at the German event.
At the St Petersburg Open, Belarusian qualifier Ilya Ivashka survived an on-court meltdown to beat French player Adrian Mannarino 6-3 7-6 (8-6) in the first round.
Trailing 3-2 in the second set, Ivashka insisted on taking a toilet break and was penalised a game on his return to court, for delaying the match.
Ivashka explained to the chair umpire he had asked for a medical timeout because he "wasn't able to stand on court", only to be told such a break could not be used for a toilet trip.
The red mist descended as a seething Ivashka shouted: "That is not possible. It is not possible."
The punishment meant the 26-year-old fell 4-2 behind in the set, but he managed to turn around the situation to progress to the last-16 stage, where Denis Shapovalov or Viktor Troicki will await.
At the same tournament, Russian Andrey Rublev began his first week as a top-10 player by scoring a comfortable 6-2 6-4 win over Canadian Vasek Pospisil.
Milos Raonic, who skipped the French Open where Rublev reached the quarter-finals, fired 21 aces in a 7-6 (7-5) 6-1 win against JJ Wolf.
In Italy, home player Lorenzo Sonego followed up his run to the fourth round of the French Open with a 6-2 7-6 (7-4) opening win over 18-year-old compatriot Giulio Zeppieri at the Sardegna Open.
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.
Auger-Aliassime won just 50 per cent of points behind his first serve as Korda claimed an impressive 6-2 6-2 success over the Canadian in one hour and 29 minutes.
In the semi-finals Korda will take on fellow American Frances Tiafoe, who edged out Alejandro Davidovich Fokina 7-6 (7-5) 5-7 7-5 in a tight encounter.
The other last-four clash will see Albert Ramos Vinolas take on Sebastian Baez.
Ramos Vinolas bested Fernando Verdasco 6-2 6-2 to set up his meeting with Baez after the Argentine rallied from a set down to defeat Richard Gasquet 3-6 6-1 6-4.
At the BMW Open, second seed Ruud fell to Botic van de Zandschulp in the quarter-finals.
The Dutchman won their only previous encounter en route to the last eight at last year's US Open and he triumphed 7-5 6-1 in Munich.
"Maybe the score is easier than it really was," said Van de Zandschulp. "The first set [was] really tight, I think. A great battle in the first one. I had some opportunities to break him in the beginning and didn't take them. Gladly [at] five-all I made the break and held the serve at 6-5.
"[The] second set was a little bit easier, but I think I played really well today."
Next up for Van de Zandschulp is Miomir Kecmanovic, who defeated Nikoloz Basilashvili 7-6 (7-5) 6-2. Holger Rune will continue his impressive run against Oscar Otte in the other semi-final after they overcame Emil Ruusuvuori and Alejandro Tabilo respectively.
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.
Verdasco, the seventh seed at the ATP 250 event played on clay, was beaten by qualifier Carlos Taberner 4-6 6-1 6-4 in Argentina.
In a clash between two Spaniards, Taberner – at 198 ranked 149 places below Verdasco – won three of the final four games.
Verdasco had made the quarter-finals in Doha and third round at the Australian Open to begin 2020, but the 36-year-old bowed out in his opener.
Sixth seed Cuevas had no such problems, beating local hope Federico Delbonis 7-5 6-2.
Earlier, Italian Gianluca Mager beat qualifier Juan Pablo Ficovich 6-2 3-6 6-2 and Attila Balazs overcame Lorenzo Sonego 6-2 7-6 (7-3).
Lajovic, who is currently ranked 37th in the world, beat 50th-ranked Paire 4-6 6-4 7-6 (7-3) in just over two hours in Buenos Aires.
In a tight match, the Serbian got the edge in the third-set tiebreak as his first serve seldom let him down.
Former top 10 player Verdasco, now 38-years-old, defeated Bolivian Hugo Dellien 6-4 3-6 6-1 in two hours and two minutes.
Serbian eighth seed Laslo Dere got past compatriot Miomir Kecmanovic 6-4 1-6 6-1, while Argentine pair Federico Coria and Francisco Cerundolo also progressed.
Meanwhile at the Dallas Open, veteran South African Kevin Anderson proved too good for Sam Querrey 6-4 6-4.
The 35-year-old former US Open and Wimbledon finalist sent down 21 aces as he won in little over an hour.
Emerging American Brandon Nakashima defeated Australian John Millman 7-5 7-6 (7-3) in the first round.
