Gent, eighth in their domestic league, went through 3-2 on aggregate after the second leg of the last-32 tie against Tottenham and will be joined in Friday's draw by Olympique Lyonnais who won 7-1 at home to AZ Alkmaar for an 11-2 triumph over two legs.
Borussia Moenchengladbach stormed back from 3-0 down on aggregate to beat Fiorentina thanks to a 12-minute hat-trick from Lars Stindl and AS Roma cruised into the next round 4-1 despite a 1-0 home defeat against Villarreal.
Europa League favourites Manchester United beat St Etienne 1-0 away on Wednesday for a 4-0 aggregate victory.
Spurs had begun in front of a record Europa League crowd of 80,465 at Wembley, where they have played European home games this term due to building work at White Hart Lane, and levelled the aggregate score after 10 minutes through Christian Eriksen.
But an own goal that glanced off the head of Spurs striker Harry Kane 10 minutes later put Gent back in the driving seat, before a moment of madness from Alli sealed Tottenham's fate.
The England midfielder showed the short fuse that was a factor in his early career as he leapt two-footed into a knee high challenge to draw a red card five minutes before halftime.
Spurs restored their advantage on the night with a thumping strike from midfielder Victor Wanyama but Jeremy Perbet, who grabbed the only goal in the first leg, scored again with a deflected effort after 82 minutes to end the hosts' hopes.
"I am very disappointed," said Tottenham's Argentine manager Mauricio Pochettino. "We started well and scored. The tie was open but we conceded a goal in one action in the first half. After that it was complicated."
Lyon's Nabil Fekir grabbed a hat-trick as the French side built on their already impressive first-leg advantage to crush Dutch side AZ by the competition's second-biggest margin, after Valencia's 10-0 defeat of Rapid Vienna last year.
[caption id="attachment_48745" align="aligncenter" width="640"]
Olympique Lyonnais' Nabil Fekir scores against AZ Alkmaar's Goalkeeper Tim Krul. REUTERS
The 13 goals over two legs also equalled the competition record, set by Porto's 10-3 win over Spartak Moscow in 2011.
Fiorentina's Nikola Kalinic and Borja Valero scored inside the first 29 minutes to give the Italians a three-goal aggregate lead before Moenchengladbach launched an improbable fightback.
Stindl converted a penalty a minute before halftime and then twice more in quick succession after the break before Andreas Christensen powered home a header on the hour to give Gladbach a 4-2 win on the night and a place in the last 16.
Four-times European champions Ajax Amsterdam went through with a 1-0 victory on Thursday and the same aggregate score over Legia Warsaw, while Celta Vigo won 2-0 at Shakhtar Donetsk after extra time to clinch a 2-1 win over the two legs.
Zenit St Petersburg beat Anderlecht 3-1 at home, but went out on away goals after the match finished 3-3 on aggregate.
Osmanlispor (TUR) 0 Olympiakos (GRE) 3
(Ansarifard 47, 86, Elyounoussi 70)
Olympiakos go through 3-0 on aggregate
Ajax (NED) 1
((Viergever 49) Legia Warsaw (POL) 0
Ajax go through 1-0 on aggregate
APOEL (CYP) 2
(Sotiriou 46, Gianniotas 54-pen) Athletic Bilbao (ESP) 0
APOEL go through 4-3 on aggregate
Zenit Saint Petersburg (RUS) 3
(Giuliano 24, 78, Dzyuba 72) Anderlecht (BEL) 1
Aggregate 3-3 - Anderlecht go through on away goals
Roma (ITA) 0 Villarreal (ESP) 1
(Borré Amaury 16)
Roma go through 4-1 on aggregate
Besiktas (TUR) 2
(Aboubakar 17, Tosun 87) Hapoel Beer-Sheva (ISR) 1
Besiktas go through lead 5-2
Fiorentina (ITA) 2
(Kalinic 15, Borja Valero 29) Borussia Moenchengladbach (GER) 4
(Stindl 44-pen, 47, 55, Christensen 60)
Moenchengladbach go through 4-3 on aggregate
Sparta Prague (CZE) 1
(Karavaev 84) Rostov (RUS) 1
Rostov go through 5-1 on aggregate
Tottenham Hotspur (ENG) 2
(Eriksen 10, Wanyama 61) Gent (BEL) 2
(Kane 20-o.g., Perbet 82)
Gent go through 3-2 on aggregate
Copenhagen (DEN) 0 Ludogorets (BUL) 0
Copenhagen go through 2-1 on aggregate
Genk (BEL) 1
(Pozuelo 67) Astra Giurgiu (ROM) 0
Genk go through 3-2 on aggregate
Lyon (FRA) 7
(Fekir 5, 27, 78, Cornet 17, Darder 34, Aouar 87, Diakhaby 89) AZ Alkmaar (NED) 1
Lyon go through 11-2 on aggregate