Mason Greenwood opened the scoring with a smart finish, writing himself into the club’s record books by becoming the youngest-ever player to score and assist in a European game at 18 years and 37 days.
The Red Devils doubled their advantage courtesy of a glorious solo goal from Anthony Martial 12 minutes before the break, as Marcus Rashford smashed in a third after the interval.
United are top of Group L, two points ahead of AZ Alkmaar, and face bottom side Astana next on 28 November.
Solskjaer can now experiment and rest key players in their upcoming European fixtures – a boost with the energy-sapping 6,000-mile return trip to freezing Kazakhstan looming large later this month.
The United boss named a strong team in a bid to get qualification wrapped up early and teenager Greenwood, one of four changes from the Cherries loss, showed excellent composure to make space and send Partizan’s goalkeeper the wrong way to open the scoring after 22 minutes.
The 18-year-old’s pressure led to the home side’s second of the evening, although Martial deserves all the credit for the way he turned superbly, evaded three challenges and slotted home a magical goal.
A thumping strike by Rashford early in the second half wrapped up victory against Savo Milosevic’s side, with the only negative for United being the sight of Scott McTominay limping off.
Thursday’s match provided entertainment too often lacking at Old Trafford this season, with both sides seeing goals ruled out for offside during the opening four minutes.
That deflected effort off Umar Sadiq was as close as Partizan would get, with Rashford fizzing wide, forcing Vladimir Stojkovic into a close-range stop and volleying over inside the opening 15 minutes.
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Murmurs of frustration followed the latter opportunity, but Rashford’s directness soon helped unlock the Partizan defence.
The 22-year-old’s pass found Greenwood in the box, with the teenager making space to hit a left-footed strike that bamboozled Stojkovic.
It was a lovely finish and United stepped up a gear after Seydouba Soumah, impressive in the return fixture, curled wide.