It was said Ole Gunnar Solskjaer's so-called honeymoon period as United interim manager was ended by the 2-0 Champions League loss to PSG, but his team bounced back in style – the Norwegian getting his tactics spot on despite the injury-enforced absences of Anthony Martial and Jesse Lingard.
Although Chelsea initially looked the brighter of the two sides, United gradually improved and was good value for the lead when Ander Herrera nodded in from close range in the 31st minute, and Paul Pogba – provider for the opener – made it 2-0 on the stroke of half-time.
In desperate need of a route back into the contest, Chelsea increased the intensity after half-time and generally controlled proceedings, but it could not find a way past the solid backline of a United side which finds itself two wins from the final.
Chelsea appeared to be shading an open contest during the early exchanges – Sergio Romero producing two saves in quick succession to keep David Luiz's free-kick and Pedro's volley out in the 11th minute.
United got a foothold and took the lead just past the half-hour mark, as Herrera beat Kepa Arrizabalaga with a stooping header from Pogba's sublime cross.
The visitor increased its lead just before half-time, as Pogba released Marcus Rashford up the right flank and then met the striker's pinpoint right-wing delivery with a towering header.
Chelsea became more productive after the interval, though United's defence thwarted it time and time again – Chris Smalling twice blocking efforts from Gonzalo Higuain.
Despite Chelsea's dominance towards the end, chances just would not present themselves and United had little difficulty holding on.