Number six seed Paire was a 6-3 7-6 (7-2) winner in his first-round match against Jozef Kovalik.
The Frenchman was not broken in the match, saving all eight of the break-point opportunities he offered up to Kovalik during a competitive 85-minute contest.
Paire's win follows a quarter-final appearance at the Hamburg European Open last week as the 32-year-old begins to recover from a dreadful first half of 2021.
Prior to his run in Hamburg, Paire had only won two ATP Tour matches this year.
Mikael Ymer had to come from behind before he progressed with a 4-6 6-3 6-3 win over lucky loser Enzo Couacaud.
The top four seeds at the ATP 250 event – led by Wimbledon semi-finalist Denis Shapovalov – get a bye through the first round and are therefore yet to begin their campaigns.
At the Croatia Open Umag, meanwhile, Radu Albot came out on top as he claimed a three-set victory over Holger Rune, with top seed Albert Ramos-Vinolas and defending champion Dusan Lajovic not in action on day one.