England striker Rooney, carrying a groin injury, watched from an executive box at Old Trafford as United piled the pressure on Chelsea ahead of their home game against Stoke City on Sunday.
United, chasing a fourth successive title, have 79 points to Chelsea's 77 with Arsenal third on 71.
Manager Alex Ferguson said Rooney, a talismanic figure for England's World Cup challenge in South Africa in June, could miss the rest of the league season. "Groin injuries are groin injuries and I think it probably will take two to three weeks (for him to recover)," Ferguson told Sky Sports television.
After a goalless first half on a scorching afternoon in Manchester, the match came alive in the final 32 minutes with Giggs scoring twice and Portuguese winger Nani delivering a killer goal.
"I think we played well. The most important thing was we kept our nerve," said Ferguson. "There were no signs of nerves whatsoever throughout the game, it was great to see that at this vital time of the season. We beat the in-form team of the week today, that says a lot for us."
Spurs went behind in the 58th minute when Patrice Evra, who was sick on the pitch at one stage in the searing heat, was brought down by a rash tackle from Cameroon defender Benoit Assou-Ekotto.
Giggs stepped up and, with all the composure of his 36 years, slotted home for his third goal of the season.
Spurs, who beat Chelsea and Arsenal last week, levelled with a 70th-minute header from Ledley King that threatened to derail United's hopes of a fourth successive title.
Nani, though, restored the home team's lead in the 81st minute after being set up by substitute Federico Macheda. The Portuguese winger was also brought down by Wilson Palacios for the 86th-minute penalty converted by Giggs.
Dimitar Berbatov, leading the attack in Rooney's absence, missed a couple of half-chances against his former Spurs team-mates in a tense opening 45 minutes but was much more influential after the break.
Close range
The Bulgarian had a close-range shot blocked by King in the 29th minute and then volleyed wide moments later.
Tottenham, who have not won in the league at Old Trafford for 21 years, remained fourth and will hope north London neighbours Arsenal beat fifth-placed Manchester City later on Saturday to prevent United's local rivals overtaking them. Spurs have 64 points, Manchester City 62.
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