The fourth seed, back in action for the first time since a surprise first-round defeat at the French Open, won 7-5 6-3 to move into the third round of the Wimbledon warm-up tournament.
Giant South African seventh seed Kevin Anderson also flourished in the warm sunshine, ending the hopes of another British player, Dan Evans, 6-2 6-3.
Dimitrov, 23, will arrive at Wimbledon as a serious contender after an impressive year that was thrown briefly off the rails by serving machine Ivo Karlovic at Roland Garros.
While disappointing, that defeat allowed the world number 13 to get in some extra days of preparation on grass - a surface ideally suited to his free-flowing game.
"No more dust on your bag and no more clay court shoes," said Dimitrov who has won two titles already this year. "It's a completely different ball game.
"I've been dwelling a little bit on it," he told reporters of his French Open defeat, "but at the same time I have it as a positive thing.
"The French was a tough moment for me. It happens but it gave me extra days out here."
And his hopes for Wimbledon?
"My goal is to be a member of Wimbledon and the easiest way to do that is win seven matches," joked Dimitrov.
It is almost a year since Cilic's world was turned upside down by a doping suspension and the 26th-ranked player is still hopeful that a strong run at Wimbledon, where he pulled out last year, can help propel him back towards the top 10.
"It's just a distant memory now," said Cilic of the darkest period of his career. "This season has been good so far for me, and now, I mean, it's open road.
"I don't have anything to defend until the end of the year so it's going to be a good part for me to focus and to try to break into the top 20 first and then later it would be nice to come closer to the top 10."
All eyes will be on Wimbledon champion Andy Murray on Wednesday when he opens the defence of his Queen's title against Paul-Henri Mathieu under the gaze of new coach Amelie Mauresmo.
Top seed Stanislas Wawrinka, who like Dimitrov fell in the first round at Roland Garros, faces wildcard Marcos Baghdatis.
2-Tomas Berdych (Czech Republic) beat James Duckworth (Australia) 7-6(3) 5-7 6-4
4-Grigor Dimitrov (Bulgaria) beat James Ward (Britain) 7-5 6-3
Sam Querrey (U.S.) beat Denis Kudla (US) 6-4 6-3
7-Kevin Anderson (South Africa) beat Daniel Evans (Britain) 6-2 6-3
Lukas Lacko (Slovakia) beat Matthew Ebden (Australia) 7-6(10) 5-7 6-4
15-Radek Stepanek (Czech Republic) beat Mikhail Kukushkin (Kazakhstan) 6-4 6-1
Victor Estrella (Dominican Republic) beat 16-Julien Benneteau (France) 6-7(3) 6-3 7-6(3)
Marinko Matosevic (Australia) beat 9-Marin Cilic (Croatia) 6-4 6-4
Denis Istomin (Uzbekistan) beat Farrukh Dustov (Uzbekistan) 7-6(9) 6-3
Marcos Baghdatis (Cyprus) beat Bradley Klahn (U.S.) 6-7(6) 6-2 6-1
Edouard Roger-Vasselin (France) beat Evgeny Donskoy (Russia) 6-3 6-7(9) 6-1
11-Vasek Pospisil (Canada) beat Paolo Lorenzi (Italy) 6-3 3-6 6-3
Jarkko Nieminen (Finland) beat Benoit Paire (France) 2-6 6-3 7-6(1)
David Goffin (Belgium) beat Dominic Thiem (Austria) 6-4 6-2
12-Dmitry Tursunov (Russia) beat Igor Sijsling (Netherlands) 6-3 6-4
10-Feliciano Lopez (Spain) beat Dusan Lajovic (Serbia) 6-3 6-7(3) 6-1
Gael Monfils (France) beat Benjamin Becker (Germany) 6-1 7-5
Teymuraz Gabashvili (Russia) beat Illya Marchenko (Ukraine) 6-7(9) 6-4 7-6(4)
Steve Johnson (US) beat Albano Olivetti (France) 6-4 6-2
Lu Yen-Hsun (Taiwan) beat Mate Pavic (Croatia) 7-6(2) 6-7(11) 7-6(5)
Ivo Karlovic (Croatia) beat 6-Mikhail Youzhny (Russia) 6-3 6-4
Alejandro Falla (Colombia) beat Lukasz Kubot (Poland) 6-2 3-6 6-3
Robin Haase (Netherlands) beat 5-Richard Gasquet (France) 6-4 6-4
- Sports & Recreation
- Marin Cilic
- Ivo Karlovic