The 29-year-old had fallen out of favour under former head coach Andre Villas-Boas, but marked his first Premier League start of the season with goals in each half at St Mary's Stadium.
Southampton made a bright start and took the lead through Adam Lallana's low drive on 13 minutes, but the sides went into half-time level thanks to Adebayor's side-footed volley.
Three goals in 10 second-half minutes followed, Rickie Lambert cancelling out Jos Hooiveld's own goal before Adebayor had the final say.
The Togolese forward produced a left-footed finish from inside the area to register his fourth goal in five Premier League outings and bolster Sherwood's chances of being appointed on a permanent basis.
Tottenham, who suffered a League Cup defeat to West Ham under Sherwood on Wednesday, now sit six points behind leaders Liverpool in seventh, while Southampton remain ninth.
Adebayor was selected alongside fellow striker Roberto Soldado in a Tottenham side showing six changes from Villas-Boas' final game in charge - a 5-0 defeat to Liverpool.
Southampton, meanwhile, brought in Lallana, Morgan Schneiderlin and Danny Fox.
The hosts initially struggled to retain possession but opened the scoring as Lallana received a pass from Fox before cleverly spinning Vlad Chiriches and placing an effort into the bottom corner from 20 yards.
Buoyed by the goal, Southampton looked comfortable and could have added a second when a flowing move resulted in Jay Rodriguez finding space in the box, only for the former Burnley man to curl his effort wide of the far post.
Tottenham capitalised on the let-off, drawing level from a counter-attack in the 25th minute when Adebayor stuck out his right boot to convert Soldado’s pinpoint cross from the left.
The visitors then operated at a high tempo when the second period got underway, and moved ahead on 54 minutes.
Neat interplay between Danny Rose and Christian Eriksen resulted in the former delivering a low cross that was diverted home by the unfortunate Hooiveld.
Southampton were level inside five minutes. Lallana timed a run to perfection behind the Tottenham defence and, as Hugo Lloris attempted to narrow the angle, laid the ball into the path of fellow England international Lambert, who passed into the empty net.
Adebayor once again stepped up for Tottenham, however, pouncing on a loose ball from Kyle Walker's long throw to grab his second in the 64th minute.
Roberto Soldado missed two clear-cut chances to make the game safe as Tottenham piled on the pressure.
The spurned chances had no impact on the outcome, however, with Southampton unable to force an equaliser.
