Having lost 1-0 in Dnipropetrovsk last week, Tim Sherwood’s side were further up against it when Roman Zozulya headed the visitors ahead shortly after the break before rallying to win 3-2 on aggregate.
But the tie swung back in their favour in 13 second-half minutes as Christian Eriksen levelled on the night before Zozulya received a red card for a headbutt on Jan Vertonghen, who tumbled to the ground very easily.
Adebayor then struck twice in four minutes to set up a mouth-watering tie with Benfica.
Jermain Defoe praised Tottenham’s fans as the England forward bade an emotional farewell to White Hart Lane. The 31-year-old has signed for MLS franchise Toronto FC and, due to a hamstring injury, was unable to take his place in the Spurs squad.
But Defoe, who has spent nine years at Tottenham over the course of two spells, emerged at half-time to say farewell to the fans.
“I’m speechless,” he said. “I’m going to miss this place. It’s been a part of my life and for my family. It’s a special place.”
Spurs face Benfica in the last 16 as the Portuguese giants completed a 4-0 aggregate win over 10-man PAOK Salonika. Nicolas Gaitan, Rodrigo Lima and Lazar Markovic struck in the last 20 minutes after the dismissal of former Benfica player Konstantinos Katsouranis.
Juventus won 2-0 at Trabzonspor to coast into the last 16 of the Europa League, 4-0 on aggregate. First-half goals from Arturo Vidal and Dani Osvaldo ensured a comfortable night for Antonio Conte’s side who now meet Serie A rivals Fiorentina.
Sevilla set up a derby showdown with arch-rivals Real Betis in the last 16 of the Europa League after seeing off the challenge of Maribor. Goals from Jose Antonio Reyes and Kevin Gameiro either side of half-time set Sevilla on their way to a 2-1 second-leg win in Spain and a 4-3 aggregate victory.
Nabil Ghilas struck an 86th-minute equaliser to send Porto to the last 16 on away goals following a thrilling 3-3 second leg draw against Eintracht Frankfurt (5-5 on aggregate).
TOTTENHAM: Lloris, Naughton, Dawson, Vertonghen, Fryers, Townsend (Lennon 85), Sandro (Bentaleb 76), Dembele, Eriksen, Soldado (Kane 88), Adebayor.
DNIPRO: Boyko, Fedetskiy (Kulakov 84), Mazuch, Cheberyachko, Strinic, Matheus, Kankava (Seleznyov 70), Rotan, Konoplyanka, Giuliano, Zozulya.
Ref: Antony Gautier (France).