After a three-hour rain delay to the start of the match, Murray added the 2013 title to those he won in 2009 and 2011 when Cilic netted a forehand after nearly two-and-a-half hours.
"I've worked very hard in the time that I had off and got myself back in the best shape possible," said Murray.
"My team helped me a lot, they were patient with me and it's why I was able to come out and play so tough in the last couple of matches.
"Marin is one of the best grass court players in the world. We've played each other since juniors and we've had a lot of close matches. I was lucky to come through at the end because he was playing such good tennis."
Murray made a blistering start to the match, breaking in just the second game with a cross court forehand winner off a shorter, defensive ball from Cilic.
At 4-2 up the Scot looked to be cruising towards the first set only to throw in a poor seventh game and allow Cilic to break back, Murray netting a forehand to concede his serve.
Things looked to be getting even worse for the world number two when he went down heavily on the baseline in the next game, slipping while trying to change direction and staying down for a while after the fall.
Cilic took the next two points to hold and fully level up the first set before breaking again in the 12th game and going on to serve out the opening set with a backhand winner.
Murray cut a distracted, frustrated figure in the early stages of the second set before eventually starting to enjoy some success against the Cilic serve in the sixth game.
But he could not take advantage of break points in that game and was forced to wait until the 13th before he made the breakthrough; stealing the Croat's serve to take the second set and level the match.
The final set was a one-sided affair, Murray cruising through his own service games before breaking in the fourth after a series of missed ground-strokes from Cilic.
A sensational running forehand passing shot winner across court at full stretch earned Murray more break points two games later, although he was unable to take either of them, while a match point followed in the seventh game.
Credit should go to Cilic, not only for battling back in the first game after being comfortable outplayed in the opening few games, but also for continuing to fight right until the very end.
The Croat saved the first match point with a big serve that Murray could only return into the net before going on to hold and force the Scot to serve it out.
Which is exactly what Murray did. An inside-out forehand approach shot winner across court earned the top seed two more match points before he sealed victory and wrapped up the title on the second when Cilic's defence finally broke down.
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