Clarke, who made 80, and Mike Hussey (44 not out) had fought a desperate rearguard action after England declared on 620-5 with a first-innings lead of 375 in the morning.
England took three Australian wickets after lunch and the Adelaide rain provided only an hour of respite for the hosts as they looked to the skies to help them avoid an innings defeat.
Pietersen, who had completed his career-best innings of 227 in the morning, was giving the specialist bowlers some rest as the day drew to a close when he made another crucial intervention.
Clarke initially walked when Alastair Cook took the catch but returned to his crease as the decision was reviewed by TV pictures. He was walking again when they clearly showed the ball hit the face of his bat.
Importantly, all the Australian batsmen played positively, refusing to simply bat for time and allow England to dictate the flow. Clarke struck 11 boundaries and Hussey, who continued his excellent series, slammed Swann over midwicket for six late in the day, ensuring that any bad balls were put away, as they would be in happier circumstances.
The only batsman who really struggled was Ponting, who was mesmerised by Swann and couldn't get off the mark until his 13th delivery. Despite punishing Swann with a vicious cut for four and a powerful sweep to the boundary, Ponting was eliminated by Swann on 9 when he played for the offspinner and edged a straighter ball low to Paul Collingwood at first slip.
The visitors would be sorely disappointed if that effort doesn't turn into a win. They'll want a lift from James Anderson, who didn't bowl at his best, while a stomach strain could keep Stuart Broad from playing much of a part on the final day. England can only hope the weather doesn't play any role either.