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Set 243 to win in 52 overs on the third and final day after the home side collapsed to 223 all out, Strauss anchored England's run chase with an unbeaten 120 to guide his side to victory with four overs and two balls to spare in a confidence booster ahead of the upcoming Ashes campaign.
The left-hander brought up his 36th first-class century with a crisp straight drive for four from the bowling of part-time spinner Michael Swart, having faced 131 balls and hit 13 boundaries.
Ian Bell, on the comeback trail after a foot injury, also looked in good touch, making 22 not out from just 18 balls as the target loomed.
Kevin Pietersen, out to put 12 months of indifferent form with the bat behind him, followed his first innings 58 with a quick-fire 35 and struck the ball far better than in his earlier knock.
He hit three glorious straight drives to the boundary in succession off pace bowler Michael Hogan and also lofted spinner Michael Beer over mid-wicket for six, before being given out leg before to Beer when attempting an audacious reverse sweep.
Pietersen, who hit five fours and a six in just 22 balls, was clearly unimpressed with the decision and stood at the crease for several seconds looking at his bat.
Aside from their disappointing top order batting performance on the second day, when they slumped to 117-7, there were plenty of positives for England.
Both Pietersen and Strauss performed well with the bat, but it was the bowling attack that most impressed ahead of the first Test in Brisbane, which starts on November 25.
Spinner Graeme Swann picked up five wickets, as did Stuart Broad, who also made a half-century with the bat in England's first innings.
James Anderson only claimed one wicket, but showed no signs of discomfort from his recent cracked rib, and young paceman Steven Finn improved as the match went on.
One concern was the form of vice-captain Alastair Cook, who failed twice at the top of the order.
Cook was clean bowled by Hogan for nine to complete a disappointing match for one of the keys to England's hopes of winning a Test series in Australia for the first time since 1986-87.
The 25-year-old, who is Strauss's vice-captain, was also bowled cheaply in the first innings, making just five.
Cook has averaged just 22.60 in his last six Tests since making centuries in successive matches against Bangladesh and has a poor record against Australia, with 498 runs at 26.21 in 10 Tests.
The home side had resumed on the third day at a commanding 109-1, an overnight lead of 128, but collapsed to be bowled out for 223.
Swann, showing no signs of discomfort after being hit on the hand during net practice earlier in the week, bowled impressively for 4-101.
Broad, who was the pick of the English bowlers in the first innings with three wickets, claimed 2-26.
Finn enhanced his claims to a berth in the first Test side, claiming the first two wickets in the WA second innings on his way to figures of 2-50.
WA captain Marcus North, looking to secure his place in Australia's first Test team, was run out by a direct hit from substitute fielder Eoin Morgan at square-leg for just one, after making 19 in the first innings.
