Jan Vertonghen handed us the dream start with the opening goal after two minutes and Gareth Bale fired home a magnificent second as we led 2-0 at half-time.
The second half burst into life on 51 minutes with three goals in 139 seconds - crucially, Clint Dempsey bagged his first goal for us, the second of those three, to restore our two-goal advantage.
At 3-2, United simply piled forward and the final half-hour seemed to last an eternity as chance after chance went begging.
William Gallas and youngster Steven Caulker were giants in central defence as we held on to clinch a landmark victory.
The first half display was as close to perfect as you can get at Old Trafford.
The lads were so good on the ball and enjoyed long spells of possession but also closed down so well, not allowing United time to breathe. We defended when we had to, broke dangerously and, most importantly, took our goals well.
Vertonghen followed his first Spurs goal at Carlisle with his first Premier League goal to hand us the ideal start in the second minute.
He played a one-two with Bale and took advantage of space opening up in front of him to dart into the box where he shifted right of Ferdinand and hit a low shot that clipped off Jonny Evans, sending Anders Lindegaard the wrong way.
Dempsey then fired a yard wide and Aaron Lennon burst from right to left before seeing his shot blocked by Evans.
It took until the 12th minute for United to threaten and Robin van Persie fired wide as William Gallas threw himself in to block.
We looked a threat on the break and that's how we opened United up for 2-0. Sandro started it by winning possession in our half, Mousa Dembele took over and rolled into Bale, sprinting over half-way. The Welsh flier sped into the box, away from Ferdinand and drilled a right-foot shot beyond Lindegaard into the far corner.
United were looking for a penalty when Nani went down under Vertonghen's challenge, but appeals were waved away and that was the end of a fantastic half for us.
As expected, Rooney entered the fray for the second half and the game exploded in the 51st minute with three goals in just over two minutes.
Rooney was inevitably involved as United pulled a goal back, his low cross to the near post touched home by Nani for 2-1.
However, we struck back immediately. Defoe did superbly wide left, controlling and spinning away from Ferdinand before releasing Bale into the box. Bale's fierce strike was parried out by Lindegaard, but Dempsey was there to tap into the empty net.
But the two-goal cushion only lasted a matter of seconds as United struck back again. Van Persie picked up the ball centrally and fed Kagawa on the edge of the box and the Japanese international clipped his finish into the far corner.
It was all United now. Rooney struck the post from a free-kick 22 yards out and then fired wide from Kagawa's pass, and Van Persie dragged a good chance across goal.
Gylfi Sigurdsson came on for Dempsey in the 70th minute but it wasn't long before van Persie had another sight of goal, this time nodding Scholes' cross wide.
Nani was next to try his luck, a snapshot that Friedel made look easy and then Gallas defended superbly, heading away as Rooney went for Nani's cross.
Danny Welbeck replaced Kagawa with 10 minutes remaining as United pushed for the equaliser, and Friedel had to be alert to parry away Scholes' blaster from 22 yards, 82 minutes on the clock.
Tom Huddlestone was next on for Dembele before another scare as Carrick flicked van Persie's corner at the near post an the ball floated onto the far post and bounced out to safety.
United's full-backs combined as Rafael's deep cross found Evra, but he couldn't direct his header far enough away from Friedel, who saved to his left.
The sight of Lindegaard in our box in the final minute upped the heartbeat a little more, but we cleared our lines for the final time for three points to remember.
Manchester United (4-3-3): Lindegaard; Rafael Da Silva, Evans, Ferdinand (Hernandez, 90+3), Evra; Giggs (Rooney, 46), Carrick, Scholes; Nani, Kagawa (Welbeck, 79), van Persie. Unused subs: De Gea, Anderson, Cleverley, Wootton.
Spurs (4-2-3-1): Friedel; Walker, Caulker, Gallas, Vertonghen; Dembele (Huddlestone, 83), Sandro; Lennon, Dempsey (Sigurdsson, 70), Bale; Defoe (90+3). Unused subs: Lloris, Falque, Mason, Townsend.
Goals: United - Nani 51, Kagawa 53. Spurs - Vertonghen 2, Bale 34, Dempsey 52.
Referee: Mr C Foy.