Adebayor grateful to Sherwood for chance
The Togolese striker struck twice in the space of four minutes as Spurs came back from two goals down in the tie with Dnipro to seal a 3-1 win on the night and progress 3-2 on aggregate.
It looked as though the hosts were crashing out when Roman Zozulya put Dnipro a goal to the good shortly after half-time, before Christian Eriksen made it 1-1 on the night with a dipping free-kick.
Spurs were given a helping hand when Zozulya used his head to negative effect, headbutting Jan Vertonghen off the ball to get a straight red card.
Tottenham - and Adebayor - capitalised in style, first converting Eriksen's cross before bringing down Ezekiel Fryers' ball and poking home.
The result set up a final-16 tie with last year's runners-up Benfica, who easily overcame PAOK 4-0 on aggregate.
Adebayor, who fell out of favour with previous boss Andre Villas-Boas, was grateful to the new manager for giving him the opportunity to play again.
"I'm very glad to be back scoring goals and happy with my team," he told ITV Sport.
"I have to keep focused and keep going. I want to say thank you to the new gaffer who came in and gave me my stage to perform.
"We knew it was going to be difficult because they had the advantage.
"But we have quality up front and on the bench. When Eriksen scored that put us on our way.
"The most important thing was to go through, and we did that so we're very happy."