Oleg Shatov's first-half goal gave Andre Villas-Boas' Zenit a 1-0 win at Standard Liege and a second-half effort from Hector Herrera was enough for the Portuguese coach's former team Porto at Lille.
Wednesday's other three matches, Slovan Bratislava-BATE Borisov, Maribor-Celtic and Aalborg-APOEL Nicosia, all ended in 1-1 draws.
Zenit's goal in the 16th minute was a superb team effort, beginning when Domenico Criscito sent a clever pass into the path of Danny.
The Portuguese player chested the ball down for Hulk and the Brazilian picked out Shatov who side-footed home from near the penalty spot.
Danny and Jose Rondon both struck the woodwork in a dominant Zenit performance
Porto, who have only missed out on the group stage four times since it started in 1992, took control of their tie when Mexico forward Herrera stabbed in from close range in the 61st minute after Vincent Enyeama had parried Jackson Martinez's header.
"We played a very serious game, against very serious and difficult opponents," said Porto coach Julen Lopetegui. "We had more than enough chances to guarantee the result and now we have to continue working to make sure of a game result in the second leg."
Slovan Bratislava gifted BATE the lead just before halftime when defender Thomas Jablonsky turned Sergei Krivets' looping cross past his own goalkeeper.
Robert Vittek grabbed a superbly taken equaliser for the Slovakian champions, who have never qualified for the group stage, with 10 minutes to play.
Celtic, who reached the playoffs after third qualifying round opponents Legia Warsaw forfeited the second leg for fielding an ineligible player, appeared determined to make the most of their reprieve in Slovenia.
They took an early lead when Callum McGregor fired in a rebound after six minutes and took the game to Maribor despite conceding an equaliser in the 14th minute when Damjan Bohar sidefooted past Craig Gordon.
Aalborg dominated the first-half against APOEL and took a deserved lead when Nicolaj Thomsen side-footed home from the edge of the area, but Brazilian Vinicius scored from the Cypriot side's only real attack nine minutes after the break.
(Writing by Brian Homewood in Berne, editing by Pritha Sarkar)
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