The second semi-final was also delayed by rain but eventually it was Lopez who prevailed after a stirring finish.
However, Muller committed another unforced error handing Querrey the mini-break advantage back, and the 2010 champion was in a good position to claim the second set by taking a 5-3 lead.
Spain's Feliciano Lopez celebrates a break point against Bulgaria's Grigor Dimitrov during the semi finals.
"It's just unbelievable to get to the final", said Cilic who won the title in 2012 and finished runner-up in 2013.
The powerful Croatian will play for a spot in the west London final against Gilles Muller, who eliminated Sam Querrey of the United States 6-4 7-6 (7-5).
Lopez erased the match point on his serve at 4-5 in the deciding set and scored the lone break of the contest in the following game before advancing in two hours and 27 minutes.
Cilic, a former U.S. Open champion, is showing good form ahead of Wimbledon, where he has reached the quarterfinals in the past three years. Lopez has also beens harp with his serve and is coming off a match in which he lost just six first serve points.
"It's tough to believe at 35 that I'm playing my best tennis, but I am".
His blistering serve had been virtually unplayable over the last week and, in four matches en route to the final, he was broken just once.
Cilic, ranked seventh in the world, is among those in with an outside chance at Wimbledon, where his aggressive game and demon serve can be exploited to the full.
"It was all a little uncertain because I don't know him that well", said Federer.
"I played great tennis this week and enjoyed every single day... it was an wonderful week and great preparation for Wimbledon". "I was waiting so long so I'm so happy today".
Having reached the Stuttgart final last week before losing to Lucas Pouille, Lopez has now won nine of his 10 matches on grass this year, raising hopes of a strong run at Wimbledon, which gets underway on July 3.
In the final, the Czech leftie will play Ashleigh Barty, an Australian who was impressive in containing former French Open champion Garbine Muguruza 3-6, 6-4, 6-2.
Cilic, who beat John Isner in round one, will now take aim at his third American in a row in the quarter-finals when he takes on unseeded Donald Young.