Swansea: Victory saw Tottenham make it five wins and a draw in the league since Sherwood replaced the sacked Andre Villas-Boas as they went level on points with fourth-placed Liverpool.
But this defeat at the Liberty Stadium meant Swansea had now gone eight league games without a win and were left just three points above the relegation zone.
Adebayor's first-half header sent Sherwood's side on their way, with Chico Flores inadvertently turning a Kyle Walker cross into his own net eight minutes into the second half to seal Swansea's fate.
<img src="http://images.mid-day.com/images/2014/jan/adebayor20jan.jpg" alt="Adebayor" /> Adebayor scores a goal. Pic/ AFP
Togo striker Adebayor made the game doubly safe, 20 minutes from time, with his second goal of the game and his fifth in his last six league games.
Wilfried Bony bagged a late consolation but it was too little, too late for the Swans.
With injuries dictating Michael Laudrup's selection, the Dane adopted a five man midfield with centre half Jordi Amat employed as one of two holding players, alongside Leon Britton.
For all the length of Swansea's winless run in the league, there were no signs of anxiety amongst the ranks early on with Jonjo Shelvey shooting wide after a training ground move from a Wayne Routledge corner.
Shelvey was off-target again after a Ben Davies break along the left and the former Liverpool midfielder went close once more in the 14th minute when he brought out the best in Hugo Lloris from 25 yards.
Sherwood wanted more from his midfield and when Britton gave away possession on half way, he got it.
Christian Eriksen picked his way through three defenders before forcing Gerhard Tremmel to pick a decent cross off the forehead of Adebayor at the far post.
At the other end, it was Bony who had hearts racing in the Spurs' back four. More clever play from &pound;12million striker created a yard of space on the edge of the box.
But when the Ivorian pulled the trigger, Lloris watched the ball skid past his far post.
He went close still to breaking the deadlock in the 24th minute when he hit the ball like an arrow only to see his 30 yard strike to rebound back off the bar with France international Lloris well beaten.
Swansea's Achilles heel this season has been their failure to score when on top and 11 minutes before half time, they once again paid the price.
Eriksen found enough time and space on the right to pick out Adebayor at the far post. Tremmel had no chance as the striker's downward header bounced up into the roof of the net.
When Shelvey limped off, five minutes after half time, Swansea were facing an even tougher battle to get back into a contest that Spurs were beginning to dominate.
Amat's frustration earned him a yellow card, for a rash challenge on Vlad Chiriches and three minutes later, a cross from Walker was turned into his own net by the unfortunate Flores.
Bony, once again, brought out the best in Lloris with a crisp shot on the hour, but it was Spurs who scored next.
Mousa Dembele missed a sitter, with only Tremmel to beat, when he might well have squared the ball to the unmarked and subsequently furious Adebayor.
But a minute later, Adebayor made no mistake after a decent through ball from Danny Rose.
Bony pounced to penalise some sloppy defending from the Spurs' back four, but it was never likely to change the final outcome.

EPL: Man United's Nemanja Vidic give up title hope

Emmanuel Adebayor scored twice as Tottenham Hotspur maintained their impressive Premier League run under manager Tim Sherwood with a 3-1 win away to Swansea on Sunday.

EPL: Adebayor double sees Tottenham down Swansea

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EPL: Adebayor double sees Tottenham down Swansea

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