Neither player was able to break serve in the match, the first at the tournament to go to three tiebreakers. Isner saved three break points and Anderson saved four.
Isner finished the match with 24 aces and Anderson had 21.
"The quality was good as far as serving goes,'' Isner said. "But other than that I think we maybe both could have played better a little bit.
"I guess it was exciting from a fan standpoint. Anytime a match comes down to a third set tiebreaker, it's going to be exciting.''
In the first round, 14th-seeded Kei Nishikori of Japan defeated Di Wu of China 6-2, 6-4.
"Obviously, it's not easy thing to play after winning the tournament,'' said Nishikori, who won the Tokyo Open on Sunday. "You want to rest. But I had a good day today.''
Also, 13th-seeded Stanislas Wawrinka of Switzerland beat Albert Ramos of Spain 7-6 (1), 7-6 (5), 15th-seeded Gilles Simon of France beat Jurgen Melzer of Austria 6-4, 6-2, and Florian Mayer of Germany defeated Bernard Tomic of Australia 6-4, 6-0.
Seventh-seeded Juan Monaco was upset by fellow Spaniard Fernando Verdasco 6-4, 6-2. The 23rd-ranked Verdasco broke his opponent three times and hold serve throughout the match.
In other first-round matches, No. 12 Milos Raonic of Canada beat Marinko Matosevic of Australia 7-6 (4), 6-3.