United, who beat Spurs on penalties in last season's Wembley final, were joined in the semi-finals by Aston Villa after the five-times winners beat Premier League stragglers Portsmouth 4-2 at Fratton Park.
Big-spending Manchester City host Arsenal while league leaders Chelsea travel to Blackburn Rovers for Wednesday's quarter-finals.
The scoreline flattered United's youthful-looking team, however, with Tottenham playing the better football for much of the first half as they sought their first win at Old Trafford in 20 years.
"We've scored against the run of play, Tottenham were I thought dominating the first 30 minutes of the match anyway," United manager Alex Ferguson told Sky Sports television. "They could have been in front by two or three opportunities.
"The second half, in fairness, we were much better. We are two games away from Wembley, so that's good...we will enjoy the semifinal and these lads will play again."
REDKNAPP STUNNED
Tottenham manager Harry Redknapp was stunned by his side's lack of passion.
"We were never going to get a better opportunity than we had tonight," he said. "The first half really, they (United) had two shots on goal and scored twice. There was no atmosphere, it was like a practice match.
"It was played at a lethargic pace, we didn't make a tackle in the first half. I've never been to Old Trafford and sensed there was no atmosphere. The thing never really got going, there was nothing happening."
Kanu pulled a goal back with a low shot in the 87th but Ashley Young restored Villa's lead two minutes later with a deflected shot high into the net.
"It was the sort of start that we didn't want," said Villa manager Martin O'Neill. "We were hoping that we could come out strongly and conceding an early goal was not part of the plan. But, if anything, it got us going."
