The Spaniard is known as the 'little beast' and he showed why as he recovered from two sets to one down and then a break down in the deciding set to win 6-3 6-7 (5/7) 2-6 6-3 7-6 (7/4) after four hours and 31 minutes.
It was also a tremendous performance from eighth seed Tipsarevic, who delighted the Arthur Ashe Stadium crowd with his superb shot-making but could not wear his opponent down.
Speaking on court afterwards, Ferrer said: "I don't have words. I'm very happy. I ran a lot. It was a really tough match. Janko is an amazing player. He fought a lot and he deserved also to win today [Thursday]."
Tipsarevic was playing in his second straight US Open quarter-final after losing to compatriot Novak Djokovic 12 months ago but was a clear underdog against Ferrer.
The relentless Spaniard has maintained the brilliant form he has shown this year and was looking to match his run here in 2007, when he lost to Djokovic in the last four.
Tipsarevic could not have made a better start, winning the opening two games, but Ferrer swiftly hit back and showed greater consistency to win the opening set.
Tipsarevic dug in well in the second, though, matching the intensity of his rival and really going for his shots.
And in the tie-break it was the Serbian who prevailed, taking his third set point with a ferocious off-forehand winner and letting out a roar of celebration.
Tipsarevic really had the bit between his teeth and he broke through to lead 3-2 in the third set after a game of spectacular rallies.
Ferrer was rattled and the eighth seed made it four games in a row to break again, and then five to clinch the set.
Tipsarevic threatened again at the start of the fourth set but Ferrer hung on, and slowly the Spaniard clawed his way back into the match.
He had his chance to break in the eighth game and he took it before levelling up at two sets all.
Tipsarevic was now looking very weary and was no doubt frustrated that, having thrown everything at Ferrer, the fourth seed was still right there.
He could not break through at the start of the decider, though, and holding on seemed to re-energise Tipsarevic, who attacked the Ferrer serve with gusto to take a 2-0 lead.
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It was another twist in this remarkable match, but not the final one, as a heavy fall at the end of the sixth game seemed to unsettle Tipsarevic and he threw in a series to errors to hand back his hard-won break.
The fourth seed scented blood and he set up two more break points at 4-4 when Tipsarevic called for the trainer for treatment to his right thigh.
He had it strapped up and promptly saved both break points before holding serve to force Ferrer to serve to stay in the match.
The Spaniard managed it twice to set up a deciding tie-break, and he struck the first blow in another brutal rally to lead 5-3.
That gave Ferrer two serves to secure victory, and he did just that, the Spaniard kneeling down on the court and screaming with delight.