In reply to the home side's first innings 385, the tourists were were all out for 251 -- a deficit of 134 runs -- 10 minutes before the scheduled interval.
Australia won the first two Tests of the five-match series in Brisbane and Adelaide and can claim the Ashes for the first time since 2007 with victory in Perth.
England resumed at 180 for four on the third morning of play and lost their last six wickets for just 71 runs.
Bell fell lbw to Harris on review, after being initially given not out by on-field umpire Marais Erasmus.
Johnson, man of the match in both of the first two Tests, had gone wicketless despite generating extreme pace, but finally broke through to have Stokes caught behind for 18 as the England newcomer chased a wide one.
Left-armer Johnson then produced one of the deliveries of the series to remove Stuart Broad for five, with a fast swinging yorker that struck the England bowler a painful blow on his right foot plumb in front of middle stump.
Tim Bresnan hit four boundaries in a breezy 21 before becoming ninth man out with the score on 233.
Graeme Swann needed treatment to his right index finger after being struck on the glove by a Siddle bouncer.
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