Rooney goals deny Spurs victory
Kyle Walker scored a free-kick to put the hosts ahead in the first half, but the England right-back haplessly set up Rooney for Manchester United's equaliser on the half hour.
Villas-Boas, whose future has come under scrutiny recently, asked his players for a response to their 6-0 defeat to Manchester City last week and he got it.
Spurs put on a far better display. Their passing was slick, their tempo high and had at least one of their many penalty shouts been given, then they would have claimed all three points.
There were chants of "AVB's blue and White Army" from the Tottenham faithful throughout the game, and the home fans applauded, rather than booed, their team off at the end.
Aaron Lennon performed superbly, Paulinho drove the midfield with his tireless energy, and even Roberto Soldado put in a good performance up front.
United were not at their best, but so long as they have Rooney in their team, they will always be capable of comebacks like this.
The faces in the dugout may have changed, but the Red Devils still have a knack of grinding out results in difficult fixtures.
Watched by England boss Roy Hodgson, Rooney's brace moved him above Robbie Fowler to become the fifth-highest Premier League scorer of all time.
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.
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 roll into the back of his net.
Villas-Boas flung his arms in the air and 33,000 jubilant Spurs fans rocked the stadium.
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.
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 denied a penalty for a handball shout inside the United box.
Soldado kicked an advertising board in frustration after ploughing a shot into the crowd.
Soldado 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 goalscorer.
Walker, caught in two minds, tapped Phil Jones' cross into Rooney's path and he stabbed the ball past Hugo 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.
Mousa Dembele nipped the ball through Jones' legs and sent Lennon rampaging forward before he went down under pressure from Patrice Evra. Again, the referee waved play on.
The game fell a little flat after the break, but Sandro had the stadium rocking again after 53 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 Danny Welbeck, but he mistimed the dive and referee 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 a 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.
Another penalty appeal was turned down in the dying seconds for Spurs and they had to settle for a draw, which was greeted by applause from their fans and club chairman Daniel Levy.
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