Edin Dzeko's hat trick helped Roma run out 4-0 winners against Villarreal at the Estadio El Madrigal.
Emerson opened the scoring just after the half-hour mark, robbing a defender of possession before unleashing a wonderful curling shot past a rooted Sergio Asenjo from 25 yards out.
Dzeko added Roma's second on 65 minutes -- Serie A's joint-top scorer rolling underneath Asenjo after collecting a pull-back Daniele De Rossi in the middle of the box.
The Bosnia international collected his second of the night and Roma's third 15 minutes later with a powerful volley after shielding off the last defender just outside the box. And he completed his treble from close range in the 86th minute.
Federico Bernardeschi's stunning free kick gave Fiorentina a 1-0 victory at Borussia Monchengladbach.
Bernardeschi smashed home from 30 yards out after being fouled by Christoph Kramer with two minutes left before the half.
Alexandre Lacazatte scored a brace as Lyon stormed to a commanding 4-1 win at AZ Alkmaar.
Lucas Tousart opened the scoring in the 26th minute, steering in a Nabil Fekir cross from a corner.
Lacazatte then added his first in first-half stoppage time after racing behind the Alkmaar back line and rounding goalkeeper Tim Krul before slotting into an empty net.
The France international bagged his brace 12 minutes after the break with a similar goal, this time using his right foot after rounding Krul.
Alireza Jahanbakhsh converted a penalty for the home side on 68 minutes to earn some consolation, but Jordan Ferri then added a fourth deep into stoppage time to give AZ an almost impossible task in Lyon for the second leg.
Russian club Rostov also put one foot in the next round by grabbing a 4-0 advantage after their home leg against 10-man Sparta Prague.
Miha Mevlja had already put the hosts in front when Tiemoko Konate was dismissed for a mistimed stamp on Timofei Kalachev in the 32nd minute.
Within 10 minutes, goals from Dmitriy Poloz and Christian Noboa had Rostov 3-0 up, and Sardar Azmoun added a fourth after half-time.
Athletic Bilbao overcame an early deficit to take control against APOEL with a 3-2 win at home.
It only took two minutes after Georgios Efrem's opener for the visitors for Mikel Balenziaga to equalise, and Aritz Aduriz put Athletic ahead on the hour mark before Inaki Williams made it a two-goal advantage.
But APOEL put themselves in decent position ahead of the second leg in Cyprus when Giannis Gianniotas got a crucial goal back in the 89th minute.
Gustavo Blanco Leschuk's strike in the 26th minute sent Shakhtar to a 1-0 win away to Celta Vigo.
Schalke secured a 3-0 victory over PAOK in Greece. Guido Burgstaller sealed the win from a free kick, sweeping home from close range after goalkeeper Panagiotis Glykos spilled Naldo's powerful header in the 26th minute.
Maximilian Meyer then scored from a header off a Benedikt Howedes cross eight minutes from time. Klaas-Jan Huntelaar capped the comfortable win moments before the final whistle.
Racing Genk secured two vital road goals in a 2-2 draw at Astra Giurgiu.
Timothy Castagne broke through the home defence in the 25th minute to give Genk an early lead, and Constantin Budescu struck just before the half to equalise for Astra.
Leandro Trossard looked to have given Genk the victory with seven minutes remaining, but Takayuki Seto scored from a header in the 90th minute to peg the visitors back once again.
FC Copenhagen led from the start and secured a 2-0 win away to Ludogorets Razgrad. Anicet Abel's second-minute own goal put the visitors ahead early.
Youssef Toutouh's goal early in the second half had the Copenhagen in control, though the hosts were able to find hope with a late strike from Claudiu Keseru, while the Danish side had Jan Gregus sent off in stoppage time.
Frank Acheampong scored twice in the first half to help Anderlecht open a 2-0 advantage from the home leg over Zenit St. Petersburg.
Olympiakos saw out a goalless draw at home against Osmanlispor despite playing the final 15 minutes a man down following Bruno Viana's dismissal.
Ajax also held on with 10 men to secure a goalless draw at Legia Warsaw after Kenny Tete was shown a red card in the 84th minute.
Earlier, Viktor Claesson marked his full debut for Krasnodar with a diving header in the fourth minute that secured a 1-0 home win over Fenerbahce.
Besiktas used an own goal to edge past Hapoel Be'er Sheva 3-1 in Israel.
William Soares handed the visitors their opener in the 42nd minute, and Elianiv Barda equalised two minutes later. But strikes from Cenk Tosun in the 60th minute and Canada international Atiba Hutchinson in second-half stoppage time sealed the win for the Turkish side.