United boss Ole Gunnar Solskjaer handed debuts to new boys Aaron Wan-Bissaka and Harry Maguire with James left on the bench while his opposite number Frank Lampard opted to start without United States international Christian Pulisic, but did name youngster Mason Mount in his line up.
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The visitors were the better team in the early exchanges and will argue the opening goal came against the run of play.
Referee Anthony Taylor played advantage following a foul by Jorginho and in the next phase of play Chelsea defender Kurt Zouma was adjudged to have fouled Rashford in the box. Following a short consultation with the video assistant referee, Taylor pointed to the spot and Rashford made no mistake.
The goal galvanised United who improved after taking the lead, but it was Chelsea who came closest to scoring when left-back Emerson Palmieri rattled David De Gea's crossbar.