He battled back from a set down and saved a match point in the deciding tie-break to win 4-6 7-6 (7/2) 7-6 (10/8) against 2012 champion Cilic, to whom he lost in straight sets at the French Open last month.
Marin Cilic has upped his record over Donald Young to an unblemished 4-0, with the highest seed left in contention at the Queen's Club grass event defeating the American 6-4, 7-5 to reach the semi-finals.
Muller will be determined to reach the final at Queens for the first time and continue his winning run on grass while Cilic will also be looking to cement his position in the run-up to Wimbledon. "I was playing really, really good throughout and Gilles was pushing me to the limit".
The 35-year-old avenged that painful loss by beating Dimitrov in the semi-finals on Saturday and now he has his hands on the trophy at last.
"(Muller) is going to be the first guy that I'm going to meet, apart from (John) Isner, serving and volleying, and obviously with his lefty serve he's really dominant on his service games on grass.
This is his first time in the semi-finals of Queens having progressed to the quarter-finals in the last two years. He saved Lopez's only break point with an ace before striking with his first opportunity to take the lead.
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Lopez's second serve hasn't been as effective, but he's been broken just once this tournament and has forced his opponent to play a near perforcent match to win.
Trailing by a set to the big-serving Cilic, Lopez held his nerve in a gripping finale to overwhelm the world number seven and secure his first ATP title since Gstaad in July 2016.
The fourth-seeded Cilic certainly looks the fresher after four singles matches this week, with Lopez initially appearing jaded against Dimitrov following his tough three-set win over Tomas Berdych in the quarterfinals.
Dimitrov saw his backhand disappear down the stretch, and he was almost up to the task of surviving without it as he saved six break points in a nine and a half minute fourth game of the set to hold for two-all. "I was waiting so long so I'm so happy today".
"I think I was playing some of my best tennis during the whole week and hopefully I can keep that running tomorrow".
Cilic kept Young under constant pressure, forcing the American to save 10 of 12 break points. "I was mixing it up really well and just playing really smart in some critical points".