Carrick struck in the 77th minute of a pulsating game after Sunderland had taken a shock lead through a brilliant Dean Whitehead free-kick and then pulled it back to 2-2 through Anthony Le Tallec after Mido and Robbie Keane had put Spurs in control.
It was harsh on Mick McCarthy's men, who have now suffered seven straight Premiership defeats and are getting isolated at the foot of the table, but they showed enough heart in this game to give them some hope of survival.
It was a thrilling match, with Keane having a penalty brilliantly saved by Sunderland's teenage keeper Ben Alnwick.
But at the end it was Spurs who took all three points to keep up their drive for a place in Europe.
Sunderland got the ideal start when Whitehead swung in a brilliant free-kick from 25 yards in the 16th minute.
Spurs equalised in the 37th minute when Mido slid in on a low cross from Keane to divert the ball over the line from close range, and Spurs had enough chances to have taken a commanding lead by half-time.
They went ahead in the 51st minute when Keane, again selected ahead of Jermain Defoe, forced his way between Alnwick and Gary Breen to knock the ball over the line for his first home goal of the season.
But Le Tallec, a substitute for the ineffective Jon Stead, got Sunderland back into it when he seized on a loose ball in the box and tucked it past Paul Robinson with a low shot into the corner of goal.
Teemu Tainio then headed against the post for Spurs, before Breen handled and Keane had his chance from the penalty spot, only for Alnwick to turn the spot-kick away at full stretch.
But Spurs were not to be denied and Carrick popped up with the winner their greater attacking efforts deserved. The midfielder took a corner on the right, and when the ball was played back to him after a clearance, he threaded a low curling shot through a crowd of legs from the tightest of angles.
Spurs hung on to confirm victory, and their fans cheered even more when they heard that rivals Arsenal had slipped up at Bolton, which allowed Tottenham to overtake them in the Champions League places.
MAN OF THE MATCH: Michael Carrick (Spurs) - Was a classy presence in the Spurs midfield and capped a fine display with a cool finish in the closing stages that finally ended Sunderland's brave resistance.