Having watched the hosts capitulate for 98 on day one, Trott ploughed on to an unbeaten 141, while wicketkeeper Matt Prior added 75 not out in a stand worth 158 by stumps.
That meant England closed on 444 for five, a position which leaves them overwhelming favourites to retain the urn by taking a 2-1 series lead with one match to play.
Ponting's anger boiled over in an ugly confrontation with both umpires, after DRS procedure ruled in Kevin Pietersen's favour over a failed caught-behind appeal. Pietersen was just one short of his 50 when Brad Haddin convinced his team-mates to review Aleem Dar's not-out decision off the bowling of Ryan Harris. No simulated evidence emerged to support Australia's review, and the initial verdict was duly confirmed.
But that did not stop Ponting, and Peter Siddle, berating Dar - and then his colleague Tony Hill - in an unseemly incident which halted play for minutes rather than seconds. It is highly likely that the under-pressure Australia captain, and Siddle too, will attract the attention of match referee Ranjan Madugalle and would be surprising, after such an unedifying spat if the umpires did not report the matter. A resulting Level 2 charge for dissent, under the International Cricket Council's code of conduct, brings with it the possibility of a one-Test ban - although a match fee fine is more often the outcome.
An eventful afternoon brought plenty more mixed emotions for Ponting, after Siddle had given Australia a much-needed kick-start on day two of this pivotal match. They began already 59 runs behind, with no English wickets down, after their hapless 98 all out yesterday. But Siddle made short work of openers Andrew Strauss and Alastair Cook, who had an unbroken stand of 157 to their name overnight but could add only another seven runs between them.
Pietersen and Trott then put on 92 together to keep England on course for a victory which would leave the series score at 2-1 in their favour and the Ashes retained. The movement of Siddle's delivery across Cook (82), for an edge and neat catch low down at slip by Shane Watson, was not outrageous.
But the delivery which did for Strauss (69) was every bit as lethal as the one his opposite number Ponting failed to cope with yesterday. Siddle got the ball to seam back at the left-hander and kick so alarmingly that it required an outstanding one-handed high catch at gully by Michael Hussey to complete the dismissal.
Events continued to go largely England's way, though - notably Pietersen surviving his controversial DRS - and Trott needing a third-umpire ruling when he almost ran himself out chancing a third run on Ponting's arm from the outfield to go to 49. But Siddle got his hands on a nearly new ball, moments after his part in the DRS altercation, and duly saw off Pietersen lbw on the back foot.
Mitchell Johnson's bouncer tactics then accounted for the out-of-form Paul Collingwood and Ian Bell, for a rare failure, when both holed out on the hook at deep fine-leg - each time to Siddle. Trott then racked up a 211-ball century despite having to hobble many of his runs after being struck on the right knee from an inside edge.
There was another kick in the teeth for Australia too when Dar again took a central role. The umpire gave Prior out for a routine caught-behind off Johnson, only to belatedly query whether the bowler had overstepped. Consultation with the third umpire confirmed a marginal no-ball, and Prior survived in bizarre circumstances to share a profitable stand with Trott.
Trott, looking in fine touch, stroked his side past 400 with a glorious cover drive off Siddle after Prior had upped the run-rate off some loose bowling from Steven Smith.
Johnson got one to leap at Prior late in the day, but the ball flew for four over and wide of the cordon. It was a rare moral victoryfor the bowlers in the final hour, as the England pair brought up new milestones - Prior's 50 and the 150 partnership included - with a series of crushing strokes.