Chelsea went ahead when Florent Malouda was fouled and Frank Lampard struck from the spot, before Ashley Young's penalty got Villa back on level terms.
Emile Heskey headed in to make it 2-1 to Villa before Didier Drogba slammed in from an angle and then John Terry slotted in late on to make it 3-2.
But there was still time for Clark to head in Marc Albrighton's cross
Full Match Highlights [ Chelsea 3-3 Aston Villa ]
Goals Video Chelsea 3-3 Aston Villa 2 January 2011