Ferrer, who was a break down early in the fifth set, won the pressure packed four-hour, 31-minute quarter-final by claiming the climactic tiebreaker 7-4 when Tipsarevic hit a backhand into the net from deep in the corner.
"I don't have words. I am really happy," said the 30-year-old Ferrer, who went down on his knees in relief after the final point before raising both fists to the cheering Arthur Ashe Stadium crowd.
"It was an emotional match. It was a really tough match. Janko is an amazing player. He fights a lot."
Ferrer will play champion Novak Djokovic of Serbia, who beat 2009 Open winner Juan Martin del Potro of Argentina, in Saturday's semi-finals.
The win was another highlight in a career season for Ferrer, who has captured five titles on three different surfaces and made at least the quarter-finals of all four Grand Slams.
"I think it was a high, intense match with not too many ups and downs," said Tipsarevic about the level of play.
"Both of us are baseline players, both of us are big fighters on court, so something like this was only expected."
Ferrer likened the intensity and emotions of the match to a Davis Cup tie and tipped his cap to Tipsarevic.
"My opponent, he deserved also to win this match," he said.
"In one tiebreak it's a lottery and I was lucky in important moments. My respect to Janko Tipsarevic."
Ferrer denied the eighth seed Tipsarevic his first trip to a Grand Slam semi-final in 35 tries but the 28-year-old Serb had nothing to be ashamed of in a hard-hitting war of attrition in which both players were treated for injuries.
The Spaniard had a right toe treated during the third set, and Tipsarevic had his left foot wrapped before the start of the final set, during which he took a sprawling fall on court and summoned a trainer to tape his right thigh.
Ferrer fell behind 3-0 in the fifth set after the Serb seized the upper hand with a second-game service break taken with a backhand volley.
The fighting spirit of Ferrer was also in full display as the Spaniard used a brilliant top-spin backhand lob to help him break back in the seventh game and put the set back on serve.
Tipsarevic looked to be on the ropes in the ninth game, facing double break point at 15-40 when he felt a twinge in his groin during the point and called for the trainer.
After getting taped up, he used two service winners and an ace to hold serve to lead 5-4.
In the next game, the Serb was within two points of victory after taking a 15-30 lead but Ferrer held him off and the two headed to a tiebreak.
The decider went on serve until Ferrer took a mini break for 5-3 when Tipsarevic could not return a shot deep to his backhand. Leading 5-4 with the next two serves on his racquet, Ferrer held firm and ended the exhausting battle.
"Now I feel tired," said Ferrer. "I have one day to rest and one day to relax. I think I am going to be good to play Saturday."