United set up a League Cup semi-final with Hull City after we brushed aside West Ham with Jose Mourinho absent from the touchline.
Anthony Martial doubled his tally for the season with a brace and Zlatan scored early and late to render former Old Trafford youth product Ashley Fletcher's goal a mere consolation.
After an impeccably observed minute's silence in memory of the Chapecoense tragedy, United made the perfect start and were ahead inside three minutes.
The goal came after superb play in the build-up from the again impressive Henrikh Mkhitaryan, who drifted away from his marker and found Zlatan with an exquisite back-heel.
Ibra was clattered by the advancing Adrian as he shaped to shoot, but made no mistake with his clipped finish for his tenth of the season.
Zlatan was denied by a fine double save from the visiting keeper after he was played in by Rooney, who then also went close with an effort from distance that Adrian tipped over the bar.
A superb lunging tackle from Marcos Rojo (yes, really) thwarted the lively Sofiane Feghouli but, out of nothing, West Ham equalised ten minutes shy of the interval.
David de Gea should have done better with Dimitri Payet's shot, but could only parry weakly and Fletcher followed up from close range to score.
United started the second half as they had the first and quickly restored their advantage three minutes after the restart.
Antonio Valencia's backheel found Mkhitaryan, who notched his second assist of the match with a fine lay-off for Martial, who finished well from ten yards.
United were dominant throughout and almost settled the tie as a contest, with West Ham again thankful to Adrian, who saved well from Martial and then Zlatan.
We did put the result beyond any lingering doubt on 62 minutes, however, when Martial lashed in following more superb link-up play with six players involved.
Referee Mike Jones waved away United appeals for a penalty when Rooney was caught by Winston Reid, before Bastian Schweinsteiger came on for his appearance since March, to a rapturous welcome.
He almost capped his dream return with a goal - but fired wide - but played a part in the fourth as United added late gloss to the scoreline.
Schweinsteiger threaded a pass through to Ander Herrera, who found Zlatan with a perfectly-flighted cross, and the Swede rolled home his second - and our fourth - in stoppage time.
The semi-finals are played over two legs, and the draw pitted us against Mike Phelan's Hull, with Southampton to take on Liverpool.
The first leg is at Old Trafford and takes place the week commencing 9th January.
Overall team performance: 9/10
United Faithful Man of the Match: Honourable mentions to Rooney, Zlatan and Martial, but we're giving this to Henrikh Mkhitaryan. Magnificent again.