Over a four-hour battle on Arthur Ashe Stadium, the 26- year-old claimed a fifth win in six matches against Tsonga, firing 29 aces and 63 winners.
But the 30-year-old Tsonga made him work in 35-degree (95 F) heat, saving four match points before the champion went through.
Croatian ninth seed Cilic goes on to face either Serbian top seed Novak Djokovic or Spanish 18th seed Feliciano Lopez for a place in Sunday's final.
He will be hoping Lopez prevails as he has a 3-2 career lead over the left-hander compared to a dismal 0-13 record against Djokovic.
"It was very hot, very demanding. I am proud that I stuck to my game plan and didn't back down."
Tsonga, who had also made the quarter-finals in 2011, went into the tie having not been broken in 56 service games at this year's US Open.
Cilic had to save four break points in the sixth game of the opener.
But it was the Frenchman who cracked first, his perfect serving run ending at 60 as Cilic converted on a fourth break point for a 5-4 lead on his way to securing the opener.
The Croatian was in complete control, sweeping into a two-set lead with Tsonga bedevilled by 14 unforced errors compared to his opponent's five.
Just as tellingly, Cilic didn't allow a single break point in the entire set.
Tsonga's mood wasn't helped by needing strapping applied to below his left knee at the changeover.
He looked doomed when he managed just three points off the first three Cilic service games of the third set, but suddenly shook himself out of his lethargy to win three games on the bounce to claim the third set.
The 30-year-old capitalised on his escape, sweeping the tie-breaker, topped off by a 13th ace of the contest.
But Cilic finished the fresher, breaking for a 3-2 lead and despite double-faulting on a fourth match point in the 10th game, he secured victory when Tsonga fired a forehand wide.
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