The 10th seed set up a second-round meeting with St Petersburg winner Martin Klizan who beat Thomaz Bellucci on Sunday.
Qualifier Kubot had no answer to the serving of 6'6" Cilic, who sent down eight aces in a match that lasted an hour and 33 minutes.
World number 11 Richard Gasquet beat Brian Baker 6-2 6-3 to progress. The Frenchman raced into a 5-0 lead en-route to taking the opening stanza and although the American did break his opponent in the second, 24 unforced errors saw him defeated in 70 minutes.
But ninth seed Nicolas Almagro of Spain was beaten in three sets by German veteran Tommy Haas.
Almagro took the opening set but Haas, ranked 21st in the world, levelled in a tie-break before two breaks of serve in the decider saw him move through to the last 32 via a 4-6 7-6 6-2 win in 123 minutes.
The top eight seeds in China including Roger Federer, Novak Djokovic and Andy Murray have received byes into the second round.
Alexandr Dolgopolov (Ukraine) beat Jeremy Chardy (France) 6-3 6-2
Andreas Seppi (Italy) beat Michael Berrer (Germany) 6-2 7-6(5)
Kevin Anderson (South Africa) beat Jarkko Nieminen (Finland) 6-2 7-6(4)
Tommy Robredo (Spain) beat Alex Bogomolov Jr (Russia) 7-6(4) 6-4
Grigor Dimitrov (Bulgaria) beat Pablo Andujar (Spain) 7-5 6-3
Sam Querrey (U.S.) beat Li Zhe (China) 6-3 6-1
Benoit Paire (France) beat Philipp Petzschner (Germany) 7-6(2) 6-4