Son Heung Min scored the only goal seven minutes from time, his long-range shot slipping through the hands of Martin Dubravka.
The result lifted Spurs one point above Manchester City, who play Monday, and four behind leaders Liverpool, who play Tuesday (both NZ time).
"It was difficult to find space," Tottenham manager Mauricio Pochettino said.
"We created some chances in the first and second half but the most important thing, in the end, is to keep pushing and it was a massive effort again in the second game consecutively. Once again I need to praise my players."
Gonzalo Higuain scored twice on his debut for Chelsea as they crushed Aaron Mooy's Huddersfield 5-0 to climb to fourth, while Wolverhampton Wanderers are seventh after a 3-1 win at Everton.
At Stamford Bridge, Higuain wasted no time making his mark after his loan move from Juventus, finding the net after just 16 minutes.
Eden Hazard scored from the spot on the stroke of halftime and grabbed his second midway through the second half.
Higuain matched the Belgian with his second three minutes later, and David Luiz wrapped things up with the fifth goal four minutes from the end.
"Higuain is improving," Chelsea manager Mauricio Sarri said.
"He wasn't physically at the top when he arrived, because he had a back problem and wasn't involved, so only played a few matches.
"He is a great player. Apart from the goals, he is really very suitable to play very close to Eden."
Ruben Neves, Raul Jimenez and Leander Dendoncker scored the goals as Wolves consolidated seventh spot in a 3-1 win at Everton.
The visitors were worthy winners, holding on despite seven minutes of extra time, played in part because a black cat ran onto the pitch in the second half.
"We are proud of the work we did," Wolves manager Nuno Esperito Samto said. "There is a long way to go and we can improve. We are not looking at the table until we go again."
Peter Crouch made his Burnley debut as a substitute at the age of 38 and earned the penalty that saw his side snatch a 1-1 draw at home to Southampton. New Zealand striker Chris Wood had earlier missed a clearcut chance for Burnley.
Crystal Palace moved up to 14th thanks to a 2-0 win over second-bottom Fulham.
Cardiff boosted their survival hopes with a 2-0 win over Bournemouth in a match that turned into a celebration of Blue Birds star Emiliano Sala, who is missing and presumed dead following a suspected plane crash.