Playing in his first match since a fourth-round loss at the US Open, the world No.49 eased past the man ranked one spot below him, reaching the second round at the event for the first time since 2016.
Tiafoe came up with the big shots when he needed them, converting four of five chances to break Paire's serve, as the veteran suffered 30 unforced errors to just 20 winners.
"I definitely took a long time off after the Open, the longest time I’ve taken in the middle of the season in a while, so [I was] a little rusty in the beginning and in the days leading up I wasn’t feeling great," Tiafoe said.
"Happy to just get a first round under my belt. Obviously tonight was up and down, Benoit wasn’t having the best of days, but you take that."
Tiafoe will face his 32nd-seeded countryman Sebastian Korda next.
Kei Nishikori, meanwhile, is among the most reliable players on the ATP Tour in deciding sets, and he prevailed in the third yet again with a 6-7 (5-7) 6-3 6-2 defeat of qualifier Joao Sousa.
Only world No.1 Novak Djokovic has a better winning percentage than Nishikori's 147-55 mark (72.8) in deciders, and the Japanese veteran put away Sousa with relative ease after dropping the first-set tie-breaker.
Nishikori hit 40 winners with 23 unforced errors in the match, to Sousa's 22 winners and 20 unforced errors. He moves on to face No.18 seed Daniel Evans in the second round.
Feliciano Lopez achieved a milestone just by stepping on the court as he set a record by appearing in his 139th ATP Masters 1000 event, one more than Roger Federer, but that was the only positive as the 40-year-old Spaniard fell to Tommy Paul 6-3 7-6 (7-3).
The 24-year-old American, ranked No.60 in the world, won 70 per cent of his service points to prevail in his Indian Wells debut.
Another tournament newcomer, Germany's Daniel Altmaier, defeated former quarter-finalist Sam Querrey 6-2 6-4 in just over an hour.
Another US veteran, Steve Johnson, lost 6-7 (5-7) 6-3 7-5 to Alejandro Davidovich Fokina, who also is playing the event for the first time.