Burnley were rarely stretched by a Port Vale side experiencing their first game under new manager, the soft-spoken Jim Gannon.
Clarke Carlisle put Burnley 1-0 up with a free header on 4 minutes, but Vale equalised with an equally soft goal - Rob Taylor poking home as their defence dithered on 15.
On 21 minutes Tyrone Mears' soft free kick slowly drifted in for 2-1, but Chris Eagles second half shot was quality for 3-1.
Lee Collins brought down Mears for a penalty scored by Graham Alexander for 4-1.
But Robert Taylor's cracking 82nd minute volley from a rebound save was equally impressive.
4-2 and out of the cup for Vale. But two goals away to a Championship side can't be bad.