Just four points separate the league leaders and Tottenham in second as United remain firmly in the hunt for a top four finish.
Chelsea’s pre-match preparations were thrown in disarray when Marcus Alonso pulled out of the warm up with Thibaut Courtois already sidelined.
And it may have had an impact just seven minutes into the clash when the outstanding Rashford fired the Red Devils ahead in controversial fashion.
Nemanja Matic’s pass hit the arm of Herrera before the midfielder slotted a wonderful pass through to the striker who outpaced David Luiz before finishing past Asmir Begovic.
The away side struggled to find any rhythm in the opening 45 minutes and frustration mounted as Diego Costa was brandished a yellow card for a late challenge on Paul Pogba.
Chelsea’s only chance of the half came from Costa whose shot from distance flew harmlessly wide.
Antonio Conte had plenty of thinking to do at half-time but just three minutes into the second period the provider turned goalscorer when Herrera’s deflected shot flew past Begovic.
Half of Old Trafford were celebrating when Rashford’s thunderbolt clattered the side netting as United looked to put Chelsea to the sword.