The Togo international scored either side of half time as he claimed the man of the match award at the Liberty Stadium, making it six goals in his last eight games.
A Chico Flores own goal also helped Spurs on their way to victory before Wilfried Bony pulled one back for the hosts late on, but Sherwood's side held on to claim their fifth straight Premier League win away from home.
Sherwood has not suffered a league defeat since taking over from Andre Villas-Boas last month and he was quick to salute the impact which Adebayor has had in recent weeks.
"It's great," he told Sky Sports. "It's obviously great for the football club and it's great for Ade himself.
"He's flying at the moment and he's enjoying his football. He's playing with a smile on his face and he's finding the back of the net."
The win in south Wales meant that Spurs moved level on points with fourth-placed Liverpool and Sherwood was delighted with the performance from his men.
"I thought we played well," he said. "Even though Swansea were having some chances from distance in the first period and they knocked it around, I thought we ironed it out in the end and got to grips with it.
"They do play a different way, they are brave on the ball, they do pass when marked and credit to them for that but we always thought that we could catch them.
"Even when they were having a lot of possession, I always thought we were the most dangerous side and it was just a matter of time before it clicked.
"We found that final ball and in the second half we could have won more comfortably."