The 125th-ranked Tiafoe had a chance to serve out the match in the fifth set, but Isner broke back and then pulled away in the final tiebreaker to win 3-6, 4-6, 7-6 (5), 6-2, 7-6 (3) in 3 hours, 27 minutes.
It was just the second career comeback from two sets down for Isner. Tiafoe had never before played a five-set match.
The 20th-seeded Isner has finished each of the past four years as the top-ranked U.S. man and has now won 11 straight Grand Slam first-round matches. He's 5-0 against fellow Americans at majors.
Tiafoe, who got in with a wild card, has just two career tour-level wins. He had played in two previous Grand Slam tournaments, losing in the first round both times.