In reply to the home team's first innings total of 385, the tourists were 180 for four at stumps on the second day, with Ian Bell on nine (from 62 balls) and Ben Stokes on 14, still trailing by 205 runs.
Australia leads the series 2-0 after wins in Brisbane and Adelaide, and can regain the Ashes with a win in Perth.
Although in-form pacemen Mitchell Johnson went wicketless despite generating express pace, all of the other Australian bowlers used took a wicket each as several English batsmen failed to build on promising starts and the effectiveness of the controversial Decision Review System was again called into question.
England were progressing steadily, if slowly, at 136-2, with Cook, who was dropped on three, grinding his way back into form.
However, the left-hander then inexplicably cut a Nathan Lyon delivery straight to Dave Warner at backward point for a soft dismissal.
It was almost identical to the way Warner fell to Graeme Swann in the Australian first innings.
Pietersen was showing unusual caution at the crease and it took him 49 balls to reach double figures.
It was the 10th time Siddle had claimed Pietersen's wicket in Test cricket, having also dismissed him twice in Adelaide in the second Test.
