It was a triumph for the Burnley substitutes for it was the quick thinking of Robbie Blake who set up the chance which Moore accepted with aplomb to earn Burnley a lucky draw.
Things had looked in good order for the Clarets when a penalty from Dean West gave them a 18th minute lead after Millwall skipper Stuart Nethercott had fouled Dimitrios Papadopoulos.
But the Lions drew level on the half hour and brilliant approach play by the outstanding Paul Ifill set up David Livermore whose right-footed half-volley was too good for Marlon Beresford.
Only a great double save from Tony Warner, first from Papadopoulos and then from Tony Grant prevented Burnley re-establishing their lead on the stroke of half time.
It was anyone's game in the second half with chances at either end and both teams had the misfortune to hit the woodwork.
Millwall winger Christophe Kinet looked on in a disbelief as Beresford managed to tip his free-kick against the crossbar and a similar fate befell Gareth Taylor, whose header clipped the top of the bar seconds later.
Another outstanding move from Millwall, again featuring Ifill, ended with Davies side-footing into an empty net before the Burnley subs combined to send the fans home at least half happy.