However, two penalties conceded by top-flight debutant Juan Foyth gave Wolves a route back into the game, and Spurs only just survived what would have been a troubling collapse against a newly-promoted club.
Wolves came into the match on the back of successive defeats but started in a confident mood as Raul Jimenez struck narrowly over the crossbar from 25 yards, and Matt Doherty worked Hugo Lloris with another shot from range.
Tottenham lost Mousa Dembele to an early injury and struggled to settle in the opening 15 minutes, although the Belgian's replacement Son Heung-min played a role in both goals as Spurs hit Wolves with a quickfire double against the run of play.
The South Korean played a one-two with Lamela, who brought down the return pass on his chest and poked a right-footed finish through the legs of Rui Patricio for his fourth goal in his last five Premier League starts.
Son was also involved in the build-up to Tottenham's second which arrived less than three minutes later, working the ball right to Kieran Trippier who stood up a cross from which an unmarked Moura could not miss his close-range header.
Tottenham's lead should have been halved before the break but Jimenez saw a goal unfortunately ruled out when the flag went up against Doherty, who was half a yard onside when he squared for the Mexican to steer past Lloris.
The Spurs captain made a string of fine saves after the restart to keep Wolves at bay, pushing away a powerful Jimenez effort and positioning himself well at his near post to block from Helder Costa, who had left Toby Alderweireld in a heap on the floor.
Lloris's best save was to deny Ruben Neves on 52 minutes, a strong hand diving low to his right at full stretch, and it looked as though the visitors had weathered the storm when Kane extended their lead at the other end.
A determined run from Lamela caught out the Wolves defence and left Kane unmarked in the middle. Although Patricio initially saved from the England striker, Kane reacted well to sweep home his first goal in four league games.
Patricio was otherwise equal to Kane's best efforts all night, saving a low piledriver across goal in the first half, and a 20-yard curler destined for the top corner on 65 minutes as Nuno Espirito Santo's side refused to give up.
Foyth gave away the first of two penalties on 68 minutes with a mistimed challenge on Jimenez, although the more experienced Trippier must share some of the responsibility for losing the ball attempting a nutmeg on his own byline.
Neves stepped up to roll the ball into the bottom corner, and Wolves were up again from the spot 10 minutes later when Foyth bundled into Jonny, and this time it was Jimenez who sent Lloris the wrong way to reduce the gap to one.
Mauricio Pochettino brought on Davinson Sanchez to try to shore things up at the back but Tottenham's defence looked very shaky right up until the final whistle, with Wolves just failing to conjure that one golden chance to equalise.
Their best opportunity from open play came in between the two penalties when Morgan Gibbs-White, influential off the bench, picked out the run of Costa with a perfectly-timed through-ball from which the winger prodded wide.
It was a lucky escape for Spurs at the end of a spell of three games in six days, albeit another victory on the road this season, and it is their away record - six wins from seven in the league - that is keeping them in touch with the pacesetters.
WOLVES (4-3-3): Patricio; Boly, Coady, Bennett; Jonny, Moutinho (Gibbs-White, 62'), Neves, Doherty; Cavaleiro (Bonatini, 62'), Costa (Traore, 84'), Jimenez
SPURS (4-3-3): Lloris; Trippier, Alderweireld, Foyth, Davies; Sissoko, Dembele (Son, 7) (Eriksen, 59'), Winks; Lamela, Lucas (Sanchez, 79'), Kane