Victory gives Jose Mourinho's Manchester United one foot in the last 16 ahead of next Wednesday's return leg.
The Swede loved playing against Les Verts throughout his four years at Paris Saint-Germain and he was at it again to take his tally in 14 games against them to 17 goals.
Ibrahimovic opened the scoring with a deflected free-kick a quarter of an hour in and had a headed effort disallowed for offside at the start of the second half.
However, he tapped in from a Marcus Rashford cutback 15 minutes from the end and wrapped things up with a penalty two minutes from time after he had been brought down in the box.
Victory gives Jose Mourinho's side one foot in the last 16 ahead of next Wednesday's return leg, although things could have been very different had Nolan Roux not spurned a chance just before United's second goal.
The win also meant United star Paul Pogba came out on top in his first competitive appearance against his elder brother, Florentin, and the world's most expensive player came close to scoring with a header that hit the bar in the second half.
Bosnian striker Edin Dzeko has been in fine form himself and he scored three times in little over 20 second-half minutes as Roma romped to a 4-0 victory away to Villarreal in Spain.
The Brazilian Emerson Palmieri gave Roma the lead with a vicious 32nd-minute hit and Dzeko then took charge in the second half, scoring the first of his three goals in the 65th minute.
Dzeko is Serie A's leading scorer with 18 goals and now has eight goals this season in the Europa League, in which Roma appear to have more than one foot in the last 16.
Tottenham Hotspur have work to do in their tie against Gent after losing 1-0 in the first leg in Belgium.
The only goal of the game came just before the hour mark when French striker Jeremy Perbet, formerly of Villarreal, scored at the second attempt from a Danijel Milicevic cutback, as Gent coach Hein Vanhaezebrouck celebrated his 53rd birthday with a win.
Tottenham goalkeeper Hugo Lloris pushed a Milicevic shot onto the post while Harry Kane had earlier struck an upright at the other end.
It was a disappointing performance from Mauricio Pochettino's side, who must now look to turn the tie around in next week's return at Wembley.
"I am disappointed because we had a lot of opportunities before we conceded, but the tie is open," Pochettino told BT Sport.
Tottenham struggled to adapt to playing 'home' games at Wembley in the Champions League, losing to Monaco and Bayer Leverkusen there.
"This is a fantastic opportunity for us to demonstrate to ourselves that we can win at Wembley and be ready for next season," when they will play all home matches there, Pochettino added.
Meanwhile, Federico Bernardeschi scored the only goal from a fine free-kick as Fiorentina won 1-0 away to Borussia Moenchengladbach.
Alexandre Lacazette found the net twice as Lyon romped to a 4-1 victory away to AZ Alkmaar in the Netherlands and Schalke also claimed a big win on the road.
The German side beat PAOK 3-0 in Greece with Klaas-Jan Huntelaar securing the win when he scored his 50th European goal late on.
Aritz Aduriz scored his seventh goal in six Europa League games for Athletic Bilbao but their 3-2 win at home to APOEL keeps the Cypriots in the tie ahead of the return.
There were also first-leg wins for Krasnodar, Rostov, Shakhtar Donetsk, FC Copenhagen, Besiktas and Anderlecht.
The Belgians beat fancied Zenit St Petersburg 2-0 in Brussels with two goals from Ghana international Frank Acheampong.