French qualifier Barrere and US veteran Isner were forced indoors by the adverse weather threat in New Zealand, with the entire Tuesday schedule taking place on inside courts and without spectators.
Despite Isner rifling down 28 aces to move 10 away from becoming the first man to post 14,000 in ATP tour and grand slam events, Barrere stuck with him and pulled off a 6-7 (3-7) 7-6 (7-5) 6-3 victory.
He snatched the only break of the match in game eight of the deciding set, before serving out for victory, with the world number 88 firing down 10 aces himself across the contest.
Argentine seventh seed Sebastian Baez also fell at the last-32 stage, bowing out 7-6 (7-1) 6-1 to American wildcard Ben Shelton.
Serbian Laslo Djere set up a second-round clash with top seed Casper Ruud by edging out Spain's Jaume Munar 3-6 6-1 7-6 (7-4), while Czech Jiri Lehecka will face second seed Cameron Norrie next after sinking Brazilian fellow qualifier Thiago Monteiro 6-3 7-5.
Ruud and Norrie received first-round byes.
At Adelaide International 2, American eighth seed Tommy Paul battled past Australian Christopher O'Connell 6-4 7-5, setting up an appetising second-round clash with Britain's Jack Draper, who won through on Monday.
There was a home success for the Australian crowd to cheer, though, as qualifier John Millman, who beat Roger Federer at the 2018 US Open, this time dug deep for a 4-6 6-3 7-6 (8-6) win against Spain's Albert Ramos-Vinolas.
World number 16 Carreno Busta, the seventh seed at the ATP 500 event in the Netherlands, took the first set with ease but fell to a 2-6 7-6 (7-2) 6-2 defeat against Frenchman Gasquet.
Veteran Gasquet, ranked 45th in the world, will next meet Stan Wawrinka after the Swiss overcame Alexander Bublik in dominant fashion with a 7-6 (7-5) 6-4 triumph.
Grigor Dimitrov recorded a 6-1 6-3 victory over Aslan Karatsev in just 59 minutes to set up a potential second-round tie with fifth seed Hubert Hurkacz, who must first get past Roberto Bautista Agut.
Qualifier Gregoire Barrere was another straight-sets winner, defeating David Goffin 6-0 7-6 (7-3).
The Frenchman, who is ranked 71st in the world, could meet third seed Felix Auger-Aliassime in the next round if the Canadian overcomes Italy's Lorenzo Sonego.
The Belarusian saw off Aljaz Bedene, with a 6-4 7-6 (7-4) win carrying him through to the quarter-finals of the Open Sud de France.
Bedene was British number two to Murray heading into Wimbledon in 2016, when the Scot won his third grand slam title, but has since reverted to representing his native Slovenia.
He put up a fight against Gerasimov, who sank Murray in straight sets on Tuesday, but the 28-year-old from Minsk took three of his five break-point opportunities and held his nerve in the tie-break to advance.
The success for Gerasimov sets up a last-eight clash with Spain's Alejandro Davidovich Fokina, who scored a fine 7-5 6-2 win over Polish fourth seed Hubert Hurkacz.
Top seed and world number 13 Roberto Bautista Agut raced to a 6-0 6-3 victory over French qualifier Gregoire Barrere, but Croatian third seed Dusan Lajovic tumbled out, losing to Dennis Novak in straight sets.
At the Singapore Open, second seed John Millman fell by the wayside, the Australian slumping 6-4 6-1 to compatriot Matthew Ebden.
French top seed Adrian Mannarino encountered no such problems, ending the hopes of Roberto Marcora with a 6-3 7-5 win to join Ebden in the quarter-finals.
Bublik's only career title to date came in Montpellier last year, but he will not defend his crown after losing in three sets to Gregoire Barrere in the first round on Wednesday.
That remarkable 6-4 6-7 (12-14) 7-6 (7-3) reverse represented Bublik's seventh loss in seven singles matches so far this season.
The 25-year-old, who has fallen to 50th in the rankings, has lost nine in a row going back to last year.
Bublik worked hard to stay in Wednesday's match in the second set, fending off three match points in the tie-break, but he could not show the same resilience in the decider as Barrere prevailed.
With the champion out, those hoping to take the title this week found life a little easier elsewhere.
Both Jannik Sinner and Alejandro Davidovich Fokina benefited from walkovers, albeit the Spaniard first had to dig in to level his match against Ugo Humbert, who had taken the opener 6-1.
Paire was drawn against compatriot Gregoire Barrere in a battle of two home hopefuls, but the more established player triumphed in straight sets.
The 20th-ranked star broke in the third game of the opener and protected his advantage in straightforward fashion.
There were no breaks in the second, but Paire dominated the tie-break to claim a 6-4 7-6 (7-1) victory.
Barrere was not the only Frenchman to exit the competition, as former world number seven Richard Gasquet went down 6-3 3-6 7-5 to Mikael Ymer.
Ymer will now meet Stefanos Tsitsipas, the defending champion and number two seed, who was granted a first-round bye.
In the final match of the day, Alexander Bublik defeated Marton Fucsovics 6-4 7-5.
