Chelsea could yet threaten the top two after beating Arsenal 2-1 to end its barren run at Stamford Bridge, but the European champions must make up an 11-point gap to United with 15 matches remaining.
Clint Dempsey rescued Spurs with a close-range strike in the third minute of stoppage time, cancelling out Robin van Persie's league-high 18th goal of the campaign that looked to be enough for United at White Hart Lane.
"We did so well at everything . the disappointment is not finishing them off," said United manager Alex Ferguson, who could find himself in disciplinary trouble for criticizing a linesman for not awarding a penalty for a foul on substitute Wayne Rooney shortly before Dempsey's goal.
Despite the draw, fourth-place Tottenham fell four points behind Chelsea in the fight for the third automatic Champions League place after goals in the opening 16 minutes by Juan Mata and Frank Lampard secured the win against Arsenal.
Dreadful in the first half, Arsenal improved after the break but couldn't add to Theo Walcott's goal in the 58th minute. Arsene Wenger's side is seven points behind Spurs, and its hopes of qualifying for the Champions League for a 16th straight season are hanging in the balance.
"We can't afford to lose more points," Wenger said. "It's a concern."
Famous for rescuing points by scoring late goals, United got a taste of what it feels like to concede in the final minutes.
Goalkeeper David De Gea failed to deal with a cross into the area and Aaron Lennon prodded the loose ball across to Dempsey, who stroked home coolly from the edge of the six-yard box. The United States forward also scored what proved to be Spurs' winner at Old Trafford in a 3-2 victory in September.
"It was a big relief," Tottenham manager Andre Villas-Boas said. "I thought we dominated the complete game.
"I think the boys have embraced the spirit that we want to be in the Champions League next year."
Van Persie continued his stunning first season at United by rising to meet Tom Cleverley's cross with a powerful header in the 25th. That was one of the few chances created by Ferguson's side, which was put under pressure after Man City's 2-0 win over Fulham on Saturday.
"Before the game we would have taken a point," United defender Rio Ferdinand said. "We have a good record here over the years, but Spurs have improved so we would have taken a point, but we are disappointed."
Playing in north London for the first time since his summer move from Arsenal, Van Persie showed once again what his former club is missing as Arsenal lost for a second straight league game.
The Dutchman's goals were the main reason why Arsenal qualified for the Champions League last season but they have found him impossible to replace.
Chelsea overwhelmed its London rival in the first half at Stamford Bridge, with Mata crashing in a fine opener in the sixth minute and Lampard slotting in a penalty after Ramires fell under the challenge of Arsenal goalkeeper Wojciech Szczesny.
The boos and jeers that have been a regular feature of Benitez's turbulent two-month tenure abated but the home crowd had to live through a nerve-wracking final half hour following Walcott's goal — his ninth in the league this season and first since signing a new contract with Arsenal on Friday.
It was Chelsea's first win in four home matches in all competitions.
"We have been doing well, creating chances in all our games," Benitez said. "In the games we didn't win, we deserved to win. It was just a matter of time until we had a performance like this."
The title may well be beyond Chelsea but the team is the favourite to finish third.
"There is a big difference between the top of the table and us," Mata said, "but we are trying."
Arsenal's game in hand is against West Ham on Wednesday.