The 20-year-old Portuguese forward scored his first goal for United since his eight-million pound transfer from Sporting Lisbon with an unstoppable 25-metre shot that took the faintest deflection off Carlos Tevez after 68 minutes.
The win lifted United up from second bottom in the table to 10th after their poor start of two draws and a defeat in their previous three league matches.
Ferguson delighted
United manager Alex Ferguson was delighted with the result and said Spurs' strong claims for a second-half penalty, when Wes Brown appeared to handle in the area, were unfounded.
The win lifted United on to five points from four matches, five points behind leaders Chelsea and two behind the other probable title hopefuls Liverpool and Arsenal. Chelsea beat Portsmouth 1-0 on Saturday to go top ahead of Manchester City, who lost top spot after losing 1-0 at Arsenal. Liverpool also won on Saturday, beating Sunderland 2-0.
In Sunday's earlier match, Newcastle United led twice but were eventually held to a 2-2 draw at Middlesbrough in a lively Tyne-Tees derby in which Mark Viduka scored his first goal for Newcastle against his former club.