The American, runner-up in Cincinnati last year, cruised to a 6-3 6-4 victory over South African Anderson.
Isner served 15 aces and broke twice in the 65-minute win at the ATP 1000 event played on hard courts.
Anderson, a quarter-finalist in Toronto last week, failed to take any of his three break points on his way to making an early exit.
The 11th-seeded Isner faces Marinko Matosevic in the second round after the fiery Australian qualifier overcame Frenchman Nicolas Mahut 6-4 7-6 (7-4).
Matosevic swore at the chair umpire, who had earlier called what appeared to be an ace on match point out, and refused to shake his hand after the win.
Spanish 16th seed Tommy Robredo also advanced after a 7-6 (7-5) 6-3 win over American wildcard Jack Sock.
Frenchman Gael Monfils progressed courtesy of a 6-3 3-6 6-3 win over Argentine Federico Delbonis.
Italian 15th seed Fabio Fognini saved two match points on his way to a 6-4 4-6 7-6 (7-5) win over Frenchman Edouard Roger-Vasselin.
Big-serving Croatian Ivo Karlovic suffered a shock 7-6 (7-5) 6-4 loss to German qualifier Benjamin Becker.
Despite 16 double faults, Fernando Verdasco got past Marcel Granollers 5-7 6-3 7-6 (7-5) in an all-Spanish encounter.
Frenchman Gilles Simon had no problems against Australian Bernard Tomic, beating the qualifier 6-3 6-2.
Germany's Philipp Kohlschreiber battled past France's Jeremy Chardy 6-3 4-6 6-4 and Pole Jerzy Janowicz defeated Russian qualifier Teymuraz Gabashvili 6-4 6-4.
Chinese Taipei's Lu Yen-Hsun easily beat Uzbek Denis Istomin 6-3 6-4 and Portugal's Joao Sousa fought past American wildcard Chase Buchanan 5-7 7-6 (7-3) 7-6 (7-5).