Southampton 1 Tottenham 4
Dele Alli's double spared Harry Kane's blushes as the midfielder helped Tottenham to an emphatic 4-1 win against 10-man Southampton.
Kane scored one but missed a penalty at St Mary's as two goals from Alli and another from substitute Son Heung-min sealed an impressive victory for Spurs.
Virgil van Dijk had earlier put Saints ahead within 73 seconds but Tottenham came back to lead after two headers from Kane and Alli.
Nathan Redmond was then sent off just before the hour by referee Mike Dean for denying Alli a goalscoring opportunity only for Kane to blaze the spot-kick over the bar.
The miss proved inconsequential, however, as substitute Son and then Alli sealed the win, which sends Tottenham back to within a point of Arsenal in fourth.
Oriol Romeu was back from suspension for Southampton while Mousa Dembele recovered from a foot problem to start for Spurs, whose only surprise selection was the missing Toby Alderweireld. The club said the Belgian had come down with a virus.
Alderweireld's absence meant Southampton fans could focus their dissatisfaction solely on Wanyama, the latest recruit to swap the south coast for White Hart Lane last summer.
Perhaps Wanyama's adrenaline was still pumping when he flew into an early challenge and moments later conceded a foul for a tug of the shirt.
James Ward-Prowse whipped in the free-kick and an unmarked Van Dijk jumped between Jan Vertonghen and Danny Rose to nod his side in front inside two minutes.
Spurs were rattled, struggling to cope with their opponents' speed out wide as Redmond motored past Dembele and drove just wide of the far post, before Sofiane Boufal tore down the left, his cross causing momentary panic as Vertonghen lashed the loose ball away from the arriving Jay Rodriguez.
If Southampton were all pace and penetration, Tottenham were more patient and precise and in the 19th minute, it paid dividends.
Dembele slid Moussa Sissoko in down the left and as the Frenchman's cross span up off Redmond, Alli reacted fastest, his glancing header nestling in the top right-hand corner.
The rest of the half was largely an exercise in attack against defence, with Alli and Christian Eriksen particularly prolific in finding space behind Southampton's midfield.
Wanyama almost put Spurs in front after he bundled his way past Van Dijk but just as the space opened up, Jose Fonte dived across to make an excellent block.
The visitors' ascendancy continued after the interval and in the 52nd minute, Kane nipped in front of Romeu and headed in Eriksen's corner for his 10th goal of the season.
There was more drama to come before the hour. On a lightning fast break, Sissoko played Alli through on goal and while the midfielder fired wide, referee Dean judged his finish to have been spoiled by a Redmond push in the back.
Dean awarded the penalty, though replays suggest the offence may have started outside the area, before compounding Southampton's misery by issuing Redmond a red card. New rules introduced in April state a team need not be punished twice for accidental fouls but deliberate fouls - which include holding, pulling or pushing - still incur a red card.
Either way, Kane failed to take advantage. The striker skied his penalty high and over the bar, before prodding the turf with his toe in disbelief.
Spurs, however, were dominant with the extra man and almost put the result beyond doubt when Eriksen crashed a shot against the crossbar.
Southampton could have snatched a late equaliser when Hugo Lloris' skewed clearance fell at the feet of Pierre-Emile Hojbjerg. The goal was temporarily open but the substitute scuffed his finish.
Instead, it was another substitute, Son, who secured Tottenham all three points as he drilled the ball into the far corner after Eriksen's through ball.
Alli then added his second and Spurs' fourth for a final flourish. Rose ghosted down the left before slipping Alli free and the midfielder curled the ball past Fraser Forster to cap a satisfying end to Tottenham's 2016.