Having been hammered 6-0 by City in their last top flight outing, Spurs were determined to offer a positive response and ease some of the pressure building on Andre Villas-Boas' shoulders.
They started brightly and took the lead after 18 minutes when Kyle Walker crashed a stinging free-kick under a leaping United defensive wall and past David de Gea before he had time to react.
The England full-back was to go from hero to villain just past the half-hour mark when he inadvertently diverted a Phil Jones cross into the path of Wayne Rooney - who gratefully gobbled up the gift to prod into the top corner.
Spurs edged back in front on 54 minutes, with Sandro crashing home a spectacular 25-yard drive into the top corner which left De Gea rooted to the spot.
Their lead was to last just three minutes, though, as Hugo Lloris tripped Danny Welbeck inside the box and Rooney made no mistake from the penalty spot as he hammered down the middle to haul the game level once more.
Villas-Boas urged Spurs fans to get behind the team in his programme notes and they responded, creating a booming atmosphere inside White Hart Lane.
The team also responded well, pressing high up the field to keep United in their own half.
Aaron Lennon was particularly impressive. The winger, chosen ahead of Andros Townsend, turned Patrice Evra inside the box, but he could only muster a weak shot with his left foot.
Spurs continued to pile the pressure on and they got their reward 18 minutes in.
Jonny Evans tripped Paulinho on the edge of the box. Walker drilled a low shot towards goal, the four men in United's wall jumped en masse and De Gea watched the ball rocket into the back of his net.
Spurs could have been 3-0 up within minutes had they had a bit of luck. Michael Dawson's volley was cleared off the line by Rooney.
Roberto Soldado then went down under pressure in the box, but no penalty was given. Villas-Boas was unhappy with the decision and moments later he stormed over to the fourth official after Spurs were again denied a spot-kick for a handball shout inside the United box.
Soldado, who had blazed over when well placed, then turned provider, playing in Lennon, but again he was forced onto his weaker foot and De Gea saved.
United could barely get into the game, but they were gifted a way back into the match thanks to a mistake from Tottenham's opening goal scorer.
Walker, caught in two minds, tapped Jones' cross into Rooney's path and he stabbed the ball past Lloris.
Spurs looked for an instant reply, but they came within an inch of going behind when Rooney lunged at Jones' wayward shot and almost diverted it past Lloris.
Sandro had the stadium rocking again after 54 minutes with a superb swerving shot that flew past a dumbstruck De Gea from 25 yards.
The lead lasted just three minutes though, and again Walker was partly to blame for the goal.
The full-back raced up the pitch to challenge for the ball deep inside the United half. United won the ball back and galloped forward. With Spurs one man down at the back, the defence looked vulnerable. Lloris raced out to challenge Welbeck, but he mistimed the dive and Mike Dean pointed to the spot.
Lloris received a yellow card and Rooney hammered the spot-kick straight down the middle to equalise.
Villas-Boas made a surprising change, bringing Townsend on for Lennon. A few Tottenham fans booed the move and there were also murmurings of discontent when Jermain Defoe replaced Soldado.
Townsend's electric pace gave Spurs an added dimension on the counter, but he was not quite quick enough to Walker's cross when Spurs hit United on a counter and the game ended level.