Chelsea 1 Tottenham Hotspur 0
United face Portsmouth at Fratton Park later in the day and anything other than a victory for the league leaders will leave them vulnerable with Chelsea still to face them at Stamford Bridge in May.
Chelsea started with intent and within seconds of the start Shaun Wright-Phillips sent over a fine right-wing cross which just escaped the diving Didier Drogba.
Chelsea almost scored on eight minutes when again Wright-Phillips arrowed a cross from the right. John Terry managed to clip the ball back from the byline to the path of Salomon Kalou, but the Ivorian blasted the ball high over the bar from ten yards out.
Carvalho met Frank Lampard's 22nd minute corner well but England goalkeeper Paul Robinson held the ball with consummate ease.
Robinson was on hand again three minutes later to halt Kalou at the far post after good approach play from Wayne Bridge and Lampard.
Wright-Phillips let fly on 31 minutes with a crisp 25 yarder but the ball swerved away from Robinson's right upright.
When Spurs made their first meaningful foray into Chelsea's penalty area on 24 minutes, Carvalho was able to snuff out Teemu Tainio's surge.
Michael Dawson prevented Lampard from volleying the opener on 38 minutes when the centre-back got his body in the way of the midfielder's right footer from eight yards out.
Robinson then made a fine low save from Carvalho to keep the Premiership champions at bay.
Chelsea had an excellent shout for a penalty on 48 minutes when Pascal Chimbonda appeared to shove Terry to the ground but referee Rob Styles waved the appeal away.
Seconds later Spurs should have scored. Hossam Ghaly headed a deep ball into the path of Mido, but Petr Cech pulled off a fine save from the Egyptian's header to tip the ball over the bar.
But Chelsea took a deserved lead on 52 minutes. Lampard fed the ball to John Obi Mikel, who in turn gave it square to his right to the in-running Carvalho. The Portugal centre-back let fly from 30 yards out and the flight of the ball deceived Robinson as it arrowed into his far corner.
Kalou could have ended the game two minutes later but Robinson redeemed himself by smothering the ball from the striker.
Robinson parried away a Drogba left-foot strike from just inside the Spurs area on 62 minutes.
Spurs boss Martin Jol made the first substitution on 64 minutes, replacing Tainio with Adel Taarabt.
Within seconds the Frenchman forced Cech into a superb low right-handed save when he shot from just outside the Chelsea area.
With nine minutes remaining substitute Dimitar Berbatov headed brilliantly on goal only to see Cech again produce a fine save to tip the ball over the bar.
Chelsea then saw out the clock for the full points and now wait to see if Manchester United slip up.