The Algerian's 86th minute intervention gave two-times runners-up Valencia a reasonable cushion for next week's second leg across the Mediterranean as they attempt to return to the group stage after a two-year absence.
Scottish champions Celtic also looked set to travel to Malmo with some breathing space but former Celtic loanee Jo Inge Berget's second goal of the night in the fifth minute of stoppage time left them the sweating with a 3-2 win.
Leigh Griffiths scored twice for Celtic with Nir Biton also on target.
"It was great to score two goals. They over-ran us in the first 10 minutes and then we calmed down a bit. The last goal is very important, it's a completely different position now," Berget, who played on loan with Celtic in 2014, told Swedish broadcaster VIasat.
Swiss club FC Basel, who reached the round of 16 last season, face a tough second leg away to Maccabi Tel Aviv after Eran Zahavi's stoppage time header earned the Israel side a 2-2 draw. Zahavi was a thorn in Basel's side all night having put Maccabi ahead before Matias Delgado drew the hosts level from the penalty spot.
Shakhtar Donetsk were 1-0 winners away to Rapid Vienna with Marlos scoring just before halftime of a frenetic game in which both sides received four bookings.
The visitors soaked up heavy pressure from the hosts either side of Marlos turning his marker and sweeping in a shot off the post.
Another late goal, scored by Josip Pivaric, gave Croatians Dinamo Zagreb a 2-1 win over Skenderbeu who now have their work cut out if they are to become the first Albanian club to play in the group stage of Europe's lucrative club competition.
Captain Blendi Shkembi had fired the home side ahead with a superb free kick but Dinamo moved up a gear after the break and equalised through Algerian striker El Arbi Hillel Soudani.
A sell-out crowd roared Valencia on against Monaco and they did not have to wait long to celebrate a goal when Feghouli headed the ball down for Rodrigo to score.
The mood changed shortly after halftime though when Mario Pasalic punished a poor clearance to equalise.
Captain Daniel Parejo restored Valencia's lead before Feghouli drove home the third.
"It's a good result, the only downside is that we conceded a goal," midfielder Parejo said.
"We're now going to Monaco to win, not just to qualify, because we don't know how to play any other way."
(Reporting by Martyn Herman, editing by Pritha Sarkar)
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