The previously out-of-favour striker hit two goals to improve Sherwood's chances of replacing Andre Villas-Boas on a permanent basis, either side of an own goal by Southampton's Jos Hooiveld. Southampton had taken an early lead through Adam Lallana before Adebayor levelled.
And although Rickie Lambert, set up by the excellent Lallana, equalised after Hooiveld's own goal, Adebayor was on hand again to wrap up the three
points. Adebayor had also scored in Sherwood's first game in charge, the 2-1 home defeat by West Ham United in the League Cup on Wednesday, but this time Spurs scored enough goals of their own to win.
The victory takes Tottenham six points ahead of Southampton and sees Sherwood's men improve the Premier League's best away record with a sixth win on the road this season. Southampton, in contrast, are without a victory in six games, equalling their longest winless sequence under manager Mauricio Pochettino.
Sherwood made four changes to the Spurs team beaten by West Ham, with captain Michael Dawson returning from suspension along with Erik Lamela, Christian Eriksen and Roberto Soldado. Southampton were worse-hit by injury and illness than had been feared.
Jose Fonte was only fit enough for the bench, while left-back Luke Shaw had succumbed to a throat ailment, leaving Dejan Lovren as the only first-choice defender in the team. But the absences did not stop the home side taking the lead after only 13 minutes.
Lovren stole the ball from Adebayor and fed Danny Fox, Shaw's replacement, on the left. He found Lallana in the centre and the England attacker was allowed to spin past Vlad Chiriches into space and line up a shot from 20 yards that sped into the bottom-left corner of the net.
Southampton missed a chance to double their lead when Danny Rose was robbed by Lambert, who slid the ball square to Lallana. He stubbed his attempt at a first-time pass, but the ball squirted through to Jay Rodriguez anyway and he should have done better than to lift the ball over the bar.
It was a costly miss. Almost immediately Adebayor hit the ball out to Soldado on the left. He reached the ball against the odds and flighted a cross to the far post where Adebayor got between Hooiveld and Fox to volley past Paolo Gazzaniga -- a goal very reminiscent of his effort against West Ham.
Early in the second half Tottenham were ahead. After 54 minutes Rose crossed low from the left and Hooiveld stuck out a foot, deflecting the ball against Gazzaniga and it trickled slowly into the back of his own net for his fourth own goal since the beginning of last season.
That might have deflated the home side, but instead they came back, Lambert sweeping the ball into an empty net in the 60th minute after Lallana, with great presence of mind, had squared the ball instead of shooting as Hugo Lloris charged from his line to narrow the angle. But there was more to come from Spurs.
Adebayor outpaced the defence to reach a long forward pass only for Gazzaniga to block his shot. And on 64 minutes, Southampton had two opportunities to clear a throw-in from the right, but failed to do so. Adebayor pounced on the loose ball, turned goalwards and found the bottom-left corner with ease.
Soldado could have made absolutely sure on two occasions, but first he got away from his marker only to pull his shot wide. And then he scooped the ball wide from two yards out after meeting Nacer Chadli's low cross from the right.