Jose Mourinho's side only had one shot in the opening 45 minutes but did not test Kepa in the Blues' net.
Chelsea on the other hand managed six attempts before the break although five of these failed to hit the target.
The one that did, though, was Antonio Rudiger's header which nestled into the far corner past United goalkeeper David De Gea.
Rudiger broke free of marker Paul Pogba and guided the ball home with 21 minutes played.
Follow the rest of the Chelsea vs Manchester United with our live blog as Mourinho's team look to salvage something from the game.
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