Fans who may have been disappointed that neither Rafa Nadal or Andy Murray featured in the last four were given plenty of compensation by a high-quality match lasting just under three hours.
Cilic will face the winner of Friday's other semi-final between seven-times Wimbledon champion Roger Federer and Czech Tomas Berdych.
Querrey, looking to be the first American to reach the final at the All England Club since Andy Roddick in 2009, had played three five-set games to reach the semi-final stage, including his quarter-final win over Murray, and he could well have taken the Croat into a decisive set.
But serving to save the match, he double-faulted and made two unforced errors before Cilic sealed victory with a forehand winner on match point.
The 28-year-old raised his arms to the sky in triumph as he celebrated becoming the first Croatian to reach the men's singles final at Wimbledon since Goran Ivanisevic in 2001.
The 2014 U.S. Open winner has been beaten in the quarter-final stage in his last three Wimbledon appearances but few would question the seventh seed's right to challenge for the title on Sunday after this display.
It was clear from the start that it was going to be a tight contest with neither player able to get even a sniff of a break in the first set.
Cilic, though, took a 4-1 lead in the tiebreak but lost five straight points as he allowed the American back into the battle.
At 6-6 there was a delay of over three minutes when a spectator fell in the stands and had to receive attention from stewards before being led out.
When play resumed Cilic produced two dreadful unforced errors with his backhand to hand the American the set and give himself plenty of work to do.
At 3-3 in the second Cilic struck, a superb backhand winner down the line on break-point giving him the advantage in the set that he never looked like losing.
When the Croat broke to go 2-1 up in the third set, the momentum seemed to have shifted decisively to Cilic with Querrey looking weary.
But the American dug deep and came out fighting - immediately breaking back and holding firm to force another tiebreak.
The contest was on-serve at 4-3 until Querrey's errors caused him to suffer two mini-breaks and the Croat took his chance.
Cilic sensed his moment but it was not until late in the fourth, with Querrey serving to stay in the match, that he grabbed it to book his place in the final.
(Reporting by Simon Evans, editing by Ed Osmond)
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