The win puts United four points ahead of third-placed Leicester, who lost to champions elect Manchester City on Saturday, while Chelsea and Tottenham both dropped points in the top-four race.
Solskjaer added: “It doesn’t really matter what anyone else does as long as we win and we get our points. We’re in second place. It’s a long way up but we want to consolidate second.”
Rashford played after being withdrawn from the England squad over the international break, having missed United’s previous three games, but succumbed to a fresh problem in the second half and grimaced as he left the pitch.
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