Trailing 2-0 at half-time with Spurs in command and United resembling a dishevelled bunch of out-of-touch strangers, the Red Devils were simply magnificent after the interval.
Carlos Tevez replaced the ineffectual Nani at the start of the second half to lead the fightback.
Wayne Rooney moved to the left and Dimitar Berbatov fell deeper behind the front three of Rooney, Tevez and Cristiano Ronaldo.
In the 57th minute, Rooney's brilliant precision pass to Michael Carrick in the Tottenham box saw the former Spurs midfielder try to round goalkeeper Heurelho Gomes.
Carrick went down as Gomes went for the ball. Whether he got a touch to it or simply brought down the United man was a borderline decision, but referee Howard Webb pointed to the penalty spot.
Spurs were furious - Gomes booked for dissent - but Ronaldo kept his cool to gently scoop the resulting kick right-footed straight and high into the roof of the net as the goalkeeper went to his left.
Paul Scholes replaced Darren Fletcher after 62 minutes and the next 17 minutes was to see the game completely turned on its head.
Ten minutes later the Red Devils were level. Berbatov fed Tevez and his cross-field pass found Rooney cutting in from the left.
Rooney fired in a left-foot shot from 12 yards which went through the legs of Vedran Corluka and into the net off Gomes' hand.
United were ahead a minute later. Rooney's cross from the left found Ronaldo diving to meet the ball with his header from four yards bouncing into the roof of the net.
Rooney made it 4-2 in the 71st minute. Berbatov touched the ball to Ronaldo and his pass from right to left picked out Rooney, who scored with a right-foot shot from ten yards despite Jonathan Woodgate's brave attempt to clear the ball on the line.
Eight minutes later, Berbatov scored against his old club. The Bulgarian found Rooney on the left and his cross into the centre was met by the languid striker.
Berbatov's header was saved by Gomes, but the ball came back off Jermaine Jenas and was touched into the net by the United striker.
It was a remarkable fightback made all the more sensational because of the first half when United were slipshod, while Spurs were slick.
With Luka Modric and Aaron Lennon running the full-backs Rafael Da Silva and Patrice Evra ragged, United were tactically naive.
Robbie Keane went deep and United's centre-backs Rio Ferdinand and Nemanja Vidic were in a quandary as to which of them would pick up lone Spurs striker Darren Bent.
It was Bent who broke the deadlock in the 29th minute with the 50th Premier League goal of his career.
Bent nipped in between Ferdinand and Vidic to take Corluka's cross from the right and, as the ball came back off Vidic, he placed it into the net right footed from eight yards.
Three minutes later, Lennon's cross from the right byline eluded the United defenders and Modric scored with a crisp left-foot shot eight yards out at the far post.