Napoli, Dynamo Zagreb, Villarreal and Valencia will take victories into next week’s second legs, while Sevilla against Slavia Prague and Eintracht Frankfurt versus Inter Milan ended all square.
First-half goals from Arkadiusz Milik and Fabian Ruiz, and an own goal by Jerome Onguene gave Napoli a 3-0 over Austrian champions Salzburg and extended their unbeaten home record in the competition to five matches.
Sevilla, who have won the Europa League three times, twice went ahead against Slavia Prague but were pegged back on both occasions in a pulsating 2-2 draw in Spain.
Wissam Ben Yedder put the home side ahead in the first minute and although Miroslav Stoch equalised with a deflected shot, Munir restored Sevilla's lead.
Alex Kral put the visitors level again six minutes before halftime when he turned a corner into the net.
Fellow Spaniards Villarreal had a happier evening in St Petersburg and will take a solid 3-1 lead over Zenit into the second leg at home.
Villarreal, third bottom of La Liga, took the lead after 33 minutes when Vicente Iborra headed home from a free kick but the home side took only two minutes to level thanks to Sardar Azmoun, whose quick thinking allowed him to stab home from close range.
The Spaniards, though, took control in the second half, with Gerard Moreno putting them 2-1 ahead after 64 minutes and Manu Morlanes added the third.
Valencia, UEFA Cup winners in 2004 and the third Spanish side left in the competition, beat Krasnodar 2-1 thanks to a first-half double from Rodrigo.
An improved second-half performance from the Russian side was rewarded with a goal by Swede Viktor Claesson.
Bruno Petkovic scored a penalty for Dinamo Zagreb to give them a 1-0 home win over Benfica while in the only game between two former winners of the UEFA Cup, Eintracht Frankfurt were held 0-0 at home by Inter Milan.
It was the first time Eintracht, who have won seven of their eight Europa League matches this season, failed to score.
The second legs take place next Thursday.