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The strikes by Rashford and Herrera at the start of each half were enough for United who, despite resting several players against Chelsea ahead of Thursday's Europa League quarter-final return leg at home to Anderlecht, were good value for their win.
A wet, cold Manchester afternoon was the setting for United to end a run of 12 games without victory against Chelsea, stretching back to a 3-2 away win in October 2012.
The striker has been United's most influential player this season, but Mourinho says the player could not make it into the starting eleven at Old Trafford.
While Chelsea are no longer the free-wheeling team seen in the weeks before Christmas, having gone nine league games without a clean sheet, they boast a formidable record against United.
Courtois is also feared to be out of the FA Cup semifinal against Tottenham later in Wembley next weekend.More news: Braves beat Padres 5-2 on opening night at new stadium
The Italian meanwhile refused to blame the absences of Marcos Alonso and Thibaut Courtois for the loss, as an overnight virus the full-back suffered disrupting Chelsea's balance, and the goalkeeper reported to have picked up an injury in a promotional TV shoot for the National Basketball Association.
Old Trafford erupted at a seventh-minute opener that Chelsea would have every right to feel aggrieved about, given Nemanja Matic saw a pass handled by Herrera in the build-up.
"Well, this season Chelsea have beaten us two times and, obviously, we don't want that to happen a third time", Pogba said.
The 19-year-old raced in behind David Luiz before clipping a shot past Begovic for his ninth goal of the season. Diego Costa was involved in a series of altercations with United's center-backs, Eric Bailly and Marcos Rojo, and could perhaps have been more severely punished on several occasions. Ashley fucking Young is captain of United???
But, four minutes into the second half, the visitors' goal was breached again.
Neither side could carve out another clear-cut chance as United went into the break leading.