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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5. Ciaran Clark - 7
Clark was much improved from the opener with West Ham. Kept the Burnley attackers at arm’s length and even got forward himself to support Lewis. Photo: Michael Regan
6. Jamal Lewis - 7
His pace made him an exciting watch going forward. He was a bit careless with the ball at times but overall, a solid display on his first competitive start since February. Photo: Ian MacNicol
7. Sean Longstaff - 6
Featured in the centre of the midfield three. Was, at times, sloppy in possession but showed desire to get on the ball. Held his nerve to dispatch his spot-kick. Photo: Ian MacNicol
8. Jeff Hendrick - 8
Hendrick was an unlikely attacking threat, wasting a great opportunity just after half-time. Probably his best performance in a NUFC shirt as he dominated the midfield. Photo: Michael Regan