Arsenal suffered a shock 1-0 defeat at BATE Borisov on a night forward Alexandre Lacazette will want to forget after being sent off late on, while Chelsea, Inter Milan and Napoli all won away in Europa League last 32 first-leg ties on Thursday.
Spanish sides Sevilla, Valencia and Villarreal also tasted victory on the road, while Benfica, Club Brugge and Plzen have the upper hand heading into next week's second legs.
Arsenal had scored 10 goals in two matches against BATE Borisov in the same competition in 2017 but never looked like being as prolific in the freezing temperatures of Belarus.
BATE took the lead when Stanislav Dragun nodded a free kick past Arsenal goalkeeper Peter Cech seconds before halftime after Lacazette put a header wide midway through the first half.
The Frenchman thought he had made up for his miss 10 minutes after the break but his effort was ruled out for offside.
To compound his misery Lacazette was shown a red card five minutes from time for felling Aleksandar Filipovic with an elbow after the defender held him back and was also booked.
Arsenal's London neighbours Chelsea did much better in similar temperatures, overcoming Malmo 2-1 in Sweden.
Ross Barkley gave the 2013 winners the lead when he stabbed home from close range on the half-hour and Oliver Giroud got his fifth goal in four Europa League matches with a slick back heel from a Willian cross 14 minutes into the second half.
Malmo's Anders Christiansen scored a lovely goal on the break to make it 2-1 but the Swedes could not level the tie.
Italian clubs also enjoyed success with Napoli beating Zurich 3-1 in Switzerland, while Inter Milan's Lautaro Martinez netted a 39th minute penalty for a 1-0 win at Rapid Vienna.
Napoli captain Lorenzo Insigne put the visitors ahead after 12 minutes as he capitalised on a dreadful mistake by keeper Yanick Brecher and Jose Callejon doubled their lead in the 21st when he slotted home from Kevin Malcuit's low cross.
Piotr Zielinski got the third 13 minutes from time before Benjamin Kololli grabbed a consolation from the penalty spot.
In the only tie featuring two teams who dropped down from the Champions League, visitors Benfica beat Galatasaray 2-1 after taking the lead in the 27th minute when Salvio converted a penalty given for handball.
Christian Luyindama equalised for the home side nine minutes into the second period but Benfica's top scorer Haris Seferovic clinched the win with a fine solo goal 10 minutes later.
It was also a good night for Spanish clubs, with Valencia, Sevilla and Villarreal winning away and Real Betis rescuing a last-gasp draw at Stade Rennes.
In Glasgow, Denis Cheryshev gave Valencia the lead against Celtic three minutes before halftime when he finished off a fine counter attack by Ruben Sobrino.
The roles were reversed in the second half when Sobrino tapped home after Cheryshev did the hard work on the break.
Alfonso Pedraza's goal after three minutes was enough to give Villarreal a 1-0 win over Sporting and maintain their unbeaten run in this year's competition.
Sevilla beat Lazio by the same scoreline in Rome thanks to Wissam Ben Yedder's close-range strike in the 22nd minute.
Real Betis were 2-0 down after 10 minutes at Rennes, a team making their first knockout round appearance in Europe.
The Spaniards got one back after 32 minutes through Giovani Lo Celso but Hatem Ben Arfa restored the home side's two-goal cushion right on halftime with a penalty.
Betis had the better of the second period and Sidnei made it 3-2 with a header before Mexican teenager Diego Lainez got the equaliser their pressure deserved just before the final whistle.
Plzen and Brugge got late goals for 2-1 home wins over Dinamo Zagreb and Salzburg respectively, while Shakhtar Donetsk twice recovered to draw 2-2 with visitors Eintracht Frankfurt.
Dynamo Kiev scored in the last minute to salvage a 2-2 draw at Olympiakos Piraeus, Russian side Krasnodar's game with visiting Bayer Leverkusen was goalless while Slavia Prague and Genk also failed to break the deadlock.
On Tuesday Fenerbahce beat Zenit 1-0.
The return legs take place on Feb. 21, except for Sevilla v Lazio, which is due to be played a day earlier.