Eighth seeded American Isner saved three match points before beating Kevin Anderson 7-6(3) 6-7(8) 7-6(7).
Isner failed to convert a match point chance in the second set tie-break and was forced into a 166 minute epic before beating the South African.
Tenth seed Cilic defeated Slovakian Martin Klizan 7-5 6-1 in 93 minutes
Klizan, a recent winner of the tournament in St Petersburg, saved eight break points in the opening set but struggled on serve throughout and was broken on four occasions.
Argentine Monaco went down to 6-4 6-2 to Spain's Fernando Verdasco.
Verdasco has slipped outside the world's top 20 after missing the summer hardcourt season because of a wrist injury but held his serve throughout the match and prevailed in 84 minutes.
The other 13 second round matches are on Wednesday with Roger Federer, Novak Djokovic and Andy Murray all in action.
Round 1 Results:
12-Milos Raonic (Canada) beat Marinko Matosevic (Australia) 7-6(4) 6-3
13-Stanislas Wawrinka (Switzerland) beat Albert Ramos (Spain) 7-6(1) 7-6(5)
14-Kei Nishikori (Japan) beat Wu Di (China) 6-2 6-4
15-Gilles Simon (France) beat Jurgen Melzer (Austria) 6-4 6-2
Radek Stepanek (Czech Republic) beat Lleyton Hewitt (Australia) 7-5 6-1
Lu Yen-Hsun (Taiwan) beat Zhang Ze (China) 6-0 6-2
Marcos Baghdatis (Cyprus) beat Fabio Fognini (Italy) 6-2 6-2
Feliciano Lopez (Spain) beat Alejandro Falla (Colombia) 6-3 1-6 6-3
Viktor Troicki (Serbia) beat Mikhail Youzhny (Russia) 6-3 2-6 6-4
Denis Istomin (Uzbekistan) beat Carlos Berlocq (Argentina) 4-6 6-2 6-1
Florian Mayer (Germany) beat Bernard Tomic (Australia) 6-4 6-0