Christian Eriksen scored twice as Tottenham maintained their challenge for a top-four finish and deepened Sunderland's relegation worries.
Patrick van Aanholt gave the Black Cats the lead against the run of play but Eriksen levelled as Lee Cattermole failed to clear on the goalline.
Mousa Dembele fired Spurs ahead before Eriksen's 25-yard shot deflected in off Sunderland debutant Jan Kirchhoff.
Harry Kane converted a penalty after Kirchhoff fouled Danny Rose.
Tottenham move a point behind third-placed Manchester City before Manuel Pellegrini's side play Crystal Palace, while Sunderland remain in the Premier League relegation places.
Although routine in the end, it was an important victory for Tottenham having lost two of their previous three home league games to fall away slightly from the leading trio of Arsenal, Leicester and Manchester City.
Mauricio Pochettino's side are now unbeaten in their past 12 league games against Sunderland, although in 11 of them they have been level at half-time.
It was difficult to fathom how that was the case on Saturday as they totally dominated the opening 45 minutes, enjoying 70% possession and 15 shots to the visitors' three.
Dutch left-back Van Aanholt, who netted against Swansea on Wednesday, beat Hugo Lloris at his near post from Adam Johnson's pass to give Sunderland an underserved lead.
Spurs were level within 91 seconds as Lee Cattermole could only deflect Eriksen's shot into the roof of the net on the goalline after Sunderland goalkeeper Jordan Pickford - making his Premier League debut - saved from Kane.
Dembele's low left-foot shot gave Spurs a 2-1 lead and they noticeably relaxed from that point, stretching away thanks to Eriksen's second and Kane's 12th league goal of the season.
Tottenham boss Mauricio Pochettino told BBC Sport: "It was a good response to the Leicester defeat. I’m very pleased. We need to be patient.
"We had a lot of shots on target – their goalkeeper was fantastic. I feel very pleased in the last few games. The belief is fantastic. We have a very good, strong squad – today was a good example."
Sunderland boss Sam Allardyce was talking to BT Sport about Jan Kirchhoff's debut, which came when he brought him on as third centre-back just before the hour mark: “Our legs were running out and I wanted to make sure we had the energy to stay in the game.
"John O’Shea and Wes Brown are in their late 30s so will feel the pace of the game. The extra defender was to tighten it up.
“It’s coming in the Premier League for the first time. He’s found out how difficult it is. We had to get him on at some stage. You can’t judge a man on one swallow. He knows what the pace is like now. He’s contributed to the loss with the penalty. But we opened up too much – that was the problem."
With BBC Sports
With BBC Sports