Published: 2017-02-17 09:36:41 BdST
United swept aside St Etienne 3-0 at Old Trafford and Roma made light work of last season's semi-finalists Villarreal with a 4-0 win in Spain, leaving their sides with little work to do in next week's return encounters.
Tottenham Hotspur's Europa League campaign, however, got off to a frustrating start as they were beaten 1-0 at mid-table Belgian outfit Gent, while Olympique Lyonnais beat AZ Alkmaar 4-1 away and Fiorentina edged Borussia Moenchengladbach 1-0.
"Every time I've played against St Etienne, with hard work there has been a couple of goals. I've scored a couple of goals tonight and hopefully I can do the same next week," Ibrahimovic told BT Sport.
He opened the scoring with a deflected free kick in the first half and added two more - a tap-in and a late penalty -after the break as United quelled the visitors' early enthusiasm.
The match was billed as a battle of the Pogba brothers with younger sibling Paul facing St Etienne's Florentin for the first time in a competitive encounter.
It was the 35-year-old Ibrahimovic who stole the show, however, grabbing his first United hat-trick and taking his tally in a remarkable maiden season at Old Trafford to 23.
Dzeko is in a similarly rich vein of form at Roma, who swatted aside a Villarreal team who are in freefall having now won just one of their last 10 games in all competitions.
Emerson Palmieri gave Roma the lead after 32 minutes and then Dzeko took over after the break, netting for the seventh straight game to double the lead in the 65th minute before adding two more goals to take his tally for the campaign to 28.
Spurs, who have dropped into the competition from the Champions League, were off colour throughout in Belgium and were undone in the second half when journeyman French striker Jeremy Perbet stroked home at the second attempt on the hour.
Spurs had arrived looking to restore pride in north London football after Arsenal were thrashed 5-1 by Bayern Munich in the Champions League on Wednesday but were stifled in a poor performance and were lucky to escape with a one-goal deficit.
Gladbach came into their encounter with Fiorentina on a hot streak having won their last four games and they dominated possession and made several chances against the Italians.
The Serie A side were resilient at the back, however, and grabbed the only goal when Federico Bernardeschi fired home a fine free kick in the dying seconds of the first half.
Lyon will take a commanding lead into their second leg against AZ Alkmaar after teenager Lucas Tousart scored his first senior goal and Jordan Ferri rounded off the scoring in stoppage time either side of Alexandre Lacazette's double.
Alireza Jahanbakhsh had reduced the deficit for AZ with a 68th-minute penalty.
Schalke 04's Klaas-Jan Huntelaar netted his 50th European goal to round off a 3-0 win at PAOK Salonika while Anderlecht overcame a sluggish Zenit St Petersburg, playing their first competitive game in 10 weeks, to win 2-0 in Belgium.
Elsewhere, Shakhtar Donetsk won 1-0 at Celta Vigo with a 27th-minute goal from Gustavo Blanco Leschuk, while Sparta Prague were thrashed 4-0 at Rostov and FC Krasnodar beat visitors Fenerbahce 1-0.