The match did not have a happy ending, with the world No.21 losing 7-6 (7-3) 7-6 (7-4) to No.1 seed Cilic.
Djokovic beat Jeremy Chardy 7-6 (5), 6-4 to advance to the Fever-Tree Championships final in London.
This was their 16th meeting and the second straight win for Marin after Paris 2016, losing the first 14 encounters against the great rival who was competing in his first ATP final since Eastbourne previous year.
Djokovic will also be well fancied for a fourth title at Wimbledon but his trophy drought now goes beyond a year - the longest time between titles in his career. I was keeping myself really focused, really composed, patient. "I was more kind of like chipping and trying to get it back in play, but it wasn't enough". I haven't played a lot of matches in the last couple of months.
The 12-time Grand Slam champion wasted an early opportunity to break before Cilic saved a match point at 4-5 and then won six points from 4-1 down in the tiebreaker to level the match. "It's easier said than done, but I'm going into tomorrow's final knowing that it's going to be a really tough match for me, but a great challenge and I'm working for it".
Cilic, whose determination has not always matched his considerable talent, heads for Wimbledon with spirits high and excellent prospects of reaching the final there again after the huge disappointment of surrendering to foot blisters and the brilliance of Roger Federer in the 2017 final.
"It's special to play here and I've played great tennis throughout the week and it's great to have another shot at the title", the 2012 Queen's champion said.
Both players are wildcards at the Nature Valley International, which starts on Monday, as they continue their comebacks from injury.
He has a 14-1 winning record over Cilic but might be second-favourite on Sunday with the Croatian in superb form.
Cilic won six points in a row to force a third set. He needed an ace to save break point in the eighth game, could do little about the angled forehand around the net that gave Cilic another chance and then dumped a tired forehand. I played a lot of three-setters and a lot of tennis.
Rybarikova twice broke the Kvitova serve in the opening set and looked a strong candidate to claim the fifth WTA tour title of her career.
Ultimately it was a backhand drive into the net that clinched the set after 67 minutes, much of which was taken up with the amount of time each player took in bouncing the ball between serves.