The Premier League champions made a bright start at the BayArena and took a deserved lead in the 22nd minute when Wayne Rooney's cross was converted by Antonio Valencia at the far post.
They doubled their advantage just eight minutes later as Rooney's free-kick was nodded into his own net by Leverkusen defender Emir Spahic.
Stefan Reinartz headed onto the post after the break for Leverkusen, but the visitors added a third when Jonny Evans tapped home in the 65th minute.
Chris Smalling scored a fourth with 13 minutes left, firing Rooney's lobbed ball into an open net, before Nani scored an exquisite late chip to consign Leverkusen to third in Group A with one match to play.
Leverkusen forward Sidney Sam – a major part of the club's best-ever start to a Bundesliga season – missed out with a thigh injury, as Reinartz and Spahic came in for the hosts.
United boss David Moyes, meanwhile, made four changes from the side that drew 2-2 at Cardiff City on Sunday, with Shinji Kagawa, Nani, Ryan Giggs and Phil Jones all drafted in.
Leverkusen immediately sat back and allowed their opponents to force the tempo, and that suited the English side, who quickly settled into their stride, with Kagawa impressing.
Nani had the game's first real chance in the 16th minute when he curled over after a clever Giggs ball, while Spahic nodded wide at the other end.
Stefan Kiessling – the Bundesliga's top scorer last term with 25 – strolled past Rio Ferdinand for the hosts and prepared to shoot, with only a last-ditch block from Evans saving the day.
And from the resulting counter-attack, United scored, as a move that involved Kagawa, Giggs and Rooney ended with the latter's ball being turned home by Valencia.
Buoyed by their opener, United pressed again and they had another goal on the half-hour mark when Spahic gave Leverkusen goalkeeper Bernd Leno no chance with a flicked header after he had been put under pressure by Smalling.
Leverkusen continued to lose the midfield battle and although Reinartz went close in the 60th minute, heading a corner onto the post, Spahic saw his follow-up well saved by United goalkeeper David de Gea.
Evans more or less sealed the victory five minutes later, pouncing quickly after Rooney's close-range effort had been parried by Leno following a corner.
There was still time for a fourth, as Rooney chipped the onrushing Leno and saw Smalling convert, while only a smart save from the Leverkusen keeper stopped Jones getting on the scoresheet himself.
However Nani's chip saw United finish with five goals as they sealed their knockout spot in fine style.
STATS ZONE Bayer Leverkusen 0-5 Man United analysis
