Rogers reached the break 114 not out with Australia 248 for seven and well on course for a thumping victory at the Sydney Cricket Ground to seal only the third 5-0 series sweep in the long history of Ashes encounters.
England's bowlers failed to make any early inroads into the Australian batting order after reducing them to 140 for four overnight and the damage was largely done when George Bailey (46), Brad Haddin (28) and Mitchell Johnson (4) were dismissed.
Although he got some help from Bailey and Haddin, Rogers will rightly take the plaudits for his second century in successive matches and his third in the 10 Ashes Tests this year.
Resuming on 73 not out, the 36-year-old, whose first and second Tests were separated by more than five years, eased towards three figures with some fluency but also the caution that was once the norm for an opening Test batsman.
Reaching 99 with a single which also brought up the 100 partnership with Bailey, he passed the milestone in style with a splendid cut past point off Kevin Pietersen's occasional spin for his 14th four.
The Sydney-born lefthander removed his helmet and raised his bat to acknowledge the warm applause from a crowd bathed in sunshine and mostly dressed in pink in honour of former bowling great Glenn McGrath's breast cancer charity.
Bailey, the only Australian player under pressure for his place in the team, departed in the next over when he miscued a pull off Stuart Broad that Scott Borthwick dived to claim at square leg.
That brought Brad Haddin to the crease and the wicketkeeper immediately showed the intent that has made him one of the players of the series, passing 3,000 Test runs before he was dismissed for 28 when he dragged a Borthwick delivery on to his stumps.
Johnson lasted three minutes before he was bowled by Ben Stokes having got all his runs in one boundary to bring out his pace-bowling partner Ryan Harris, who was one not out at the break.
With more than half of the match still remaining, Australia can afford to bat on as long as they like before unleashing their potent pace attack on an England batting line-up that has failed to fire in this series.