England set their stall out, in a succession of public statements, to win each of their tour matches before this month's first Test in Brisbane.
They were hardly well-set to do so at start of play on the final day of three against Western Australia, their hosts 109 for one and already 19 more to the good via two first-innings declarations.
But Strauss' attack upped their game to take eight wickets for 64 runs and bowl WA out for 223 just after lunch - and then he led the way as the batsmen knocked off 242 in 52 overs with 4.1 to spare and six wickets in hand.
The captain saw the job through with 15 fours and a six from 141 balls at the WACA Ground, and there were useful runs too from Kevin Pietersen - with only Strauss' opening partner Alastair Cook missing out in both innings.
"We're very pleased, especially because of the position of the game at start of play," Strauss said. "It was looking like a tough 'ask' to force a result from there. But we had two choices. We could have come here and gone through the motions today - but what we did was come in and hit the ground running."
A tailend partnership between Stuart Broad and Graeme Swann bailed England out in the first innings, after only Pietersen had impressed higher up.
With ball in hand, Broad was convincing throughout; Swann ended up with five wickets in the match and paceman Steven Finn improved dramatically on the final morning.
"Steven bowled an outstanding spell right from the start, and we got some momentum," added Strauss. "We're delighted with the way the bowlers bowled, and it was a good effort from the batters to chase down that score.
"Steven was rusty in the first innings, but got better as it went on. James Anderson and Broad were spot on in that first innings. But Finny really set the tone today, consistent length-wise and caused all the batsmen some trouble.
"That was really encouraging, as was the way the bowlers bowled in partnerships and applied pressure. That's what you've got to do out here."
Strauss chose not to crow about his own significant contribution, his first senior hundred in Australia.
"It's important we play well and win as many of these games as possible; it's also important that batsmen get used to the conditions," he said. "The best way to do that is by spending a lot of time in the middle. It was satisfying to get a hundred and see the guys home.But I'm sure there are sterner tests ahead."
Strauss found particular encouragement in his team's evident all-round progress in the course of the match.
"None of us have played any cricket for a few weeks," he added. "In the first innings, I thought we got stuck in net mode a little bit and probably didn't react as well to the conditions as we could have done. We were better second time round, and I hope we should get better with every innings we play.
"These conditions are different to England, so your shot selection has to be slightly different and the balls you score off are slightly different. There are times you've got to be patient, probably more so than in England."
The tourists could hardly have been sensing victory until WA's middle order imploded. Perhaps the most telling moment came when substitute fielder Eoin Morgan, on the field for just one over while Strauss took a "comfort break", ran out home captain Marcus North for a single with a direct hit.
North's opposite number could hardly take any credit for that sequence of events but was able to reflect with good humour on the turning point.
"I was in the loo actually," Strauss confirmed. "It was an inspired bit of captaincy on my part."