Steve Bruce’s side should have been home and dry in normal as they had the Clarets defence on the ropes.
However, Sean Dyche’s side held out for spot-kicks, where they emerged victorious after goalkeeper Wayne Hennessey saved Allan Saint-Maximin and Miguel Almiron’s efforts.
Here’s how we rated each United player as the club’s long wait for a major trophy continues:
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13. Allan Saint-Maximin (on for Gayle, 75)
Regularly dispossessed by Burnley’s sliding tackles. Missed United’s opening spot-kick of the evening.
Photo: Ian MacNicol
14. Miguel Almiron (on for Fraser, 83)
The Paraguayan never looked confident from the spot - and so that proved as Hennessey saved before Charlie Taylor netted the decider.
Photo: George Wood