The champions, poised to make their worst start to a league season since Sir Alex Ferguson came to the club in November 1986, had the diminutive winger to thank for their victory.
With United looking far from certain of even taking a point, another new signing Carlos Tevez laid the ball back to Nani from the edge of the Tottenham box in the 68th minute.
And Nani, who cost the Reds £17.3million from Sporting Lisbon in the summer, controlled the ball before hitting a vicious, swerving 30-yard right-foot shot which stung the fingertips of Spurs goalkeeper Paul Robinson on its way into the roof of the net.
It brought United their first win of the campaign and was their first Premier League goal at Old Trafford in 335 minutes.
Had United not won, it would have been their worst opening four games of a season since 1986/87 when Ron Atkinson lost his job to Ferguson.
Spurs deserved at least a draw and could point to a controversial decision by referee Howard Webb three minutes before the United goal.
Steed Malbranque picked out Dimitar Berbatov on the right side of the United box.
United goalkeeper Edwin Van der Sar failed to clear from the rampaging Bulgarian who chipped his shot towards the net.
The ball hit the chest and then appeared to strike the arm of Wes Brown from close range, although it was difficult to see how the United defender could have got out of the way in time.
Mr Webb ruled that the handball was unintentional and waved away the vociferous Tottenham protests.
Tottenham, whose manager Martin Jol is under somewhat unfair pressure, has now seen his side lose three of their opening four games.
But the amiable Dutchman could point to two other incidents which, on another day, would have brought his side at least one goal.
The first came after only 18 seconds when Berbatov's back-heel set up Robbie Keane to hit a 25-yard shot which beat Van der Sar before rattling the United bar.
The second resulted from a bizarre 64th minute incident.
United defender Nemanja Vidic gave the ball away to Gareth Bale as he raced through the middle.
Bale played the ball towards Berbatov racing into the Reds Devils' penalty area and Vidic hurled himself forward to try and cut it out.
Berbatov stuck out his foot and touched the ball past Van der Sar and it seemed to be rolling into the net until a last ditch clearance by Rio Ferdinand saved the day for United.
The goal apart, United had two other clear chances.
The first came when Robinson denied Ferdinand from point-blank range in the 21st minute and the second was seconds before United's winner when Tevez's 20-yard shot was cleared off the Tottenham line by Jermaine Jenas.