White's century featured a six and nine fours. He faced 124 balls, batted calmly throughout and only took risks when the situation demanded.
His performance under the Hampshire floodlights will surely guarantee his place when Ricky Ponting returns to lead Australia for the final four matches of the series.
But England, who batted poorly for the third time in succession, will have to make changes. It was particularly perplexing to see Yorkshire youngster Adil Rashid overlooked for the second game in succession in an unchanged side.
Strauss's good fortune at the toss continued, winning his third from three of this series to go with four out of five in the Ashes.
Unlike the two defeats in London, however, here the England captain elected to bat first, and Clarke revealed he would have done the same.
On a wicket lacking pace, and thus drawing the sting out of Brett Lee, England got off to a fast start.
Strauss pulled, drove and cut Lee to score 12 from three balls, while Ravi Bopara lofted a straight drive off Nathan Bracken for six.
England had advanced to 41 without loss in the eighth over when Bopara attempted a repeat off Bracken, but with wicketkeeper Tim Paine now standing up to the stumps he stayed in his crease. He was consequently not to the pitch of the ball and this time lobbed up a catch to mid-on.
Strauss was badly let down by his top-order colleagues
Matt Prior's poor run with the bat continued when he pulled his fourth ball to square-leg, while Owais Shah got a bad lbw decision and that left England 62-3 in the 15th.
All the while, Strauss had again looked in great nick, but when he chipped Nathan Hauritz to short mid-wicket on 63, England were 98-4 with almost half their overs gone and the top order had dug an unwelcome hole for the rest of the team to get out of.
That they partly did so was initially down to Eoin Morgan, who made 43, his best yet for England - before he perished in the final powerplay to the expensive Lee.
Shane Watson was the pick of the Australian bowlers with 3-36, but could not prevent the ninth-wicket pair of Bresnan (31 not out) and Ryan Sidebottom (24) from adding 40 from the last 39 balls of the innings.
It was a timely boost which at least gave England's bowlers something to work with, and when Anderson's lbw appeal against Watson was upheld in the fifth over there was more for the home fans to smile about.
But after a slow start (29-1 from 10), Paine and White opened the throttle for a few overs to put the pressure back on the hosts.
Paul Collingwood responded to the challenge, trapping Paine lbw for 29 in the 14th over, whereupon the incoming batsman Clarke was almost run out for a single, Shah missing the stumps from the same angle that Andrew Flintoff had run out Ponting on the last day of the Ashes.
In his last match as stand-in skipper, Clarke batted patiently
White targeted Collingwood for some treatment, and when 10 precious runs came off the 20th over Australia were well set on 79-2.
But England remained determined to build pressure, and that set up another golden opportunity for a run-out, with White on 46 the man to survive. This time Anderson was the fielder, hurrying his shy from a few feet away when he probably had time to dive at the stumps with ball in hand.
White cruised past 50 and initially prevented the required rate going past six with nine more runs in a Graeme Swann over. But Clarke continued to struggle with his timing, leaving 75 wanted from the last 66 balls - Anderson having again been involved in a failed run-out attempt.
The batting powerplay was taken and White now smashed Sidebottom over mid-on for Australia's first six of the series. He got lucky when Bresnan dropped a sitter at long-on and duly went on to notch the first century by any player in what has been an underwhelming series.
Clarke was finally bowled by Swann, and White holed out to Wright, who was probably the best of England's bowlers, though Strauss only gave him seven overs.
Callum Ferguson and Michael Hussey then batted smartly to prevent any final-over drama.
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