Australia were 92 for two at lunch on the first day, with Rogers a Test-best 67 not out and Australia captain Michael Clarke unbeaten on five after yet another controversial Decision Review System (DRS) verdict this series contributed to the dismissal of Usman Khawaja.
Top-order batting has long been the Achilles heel of an Australia side who came into this match 2-0 down in the series and on a losing streak of six straight Tests - their worst run since 1984 - following a 4-0 loss in India earlier this year.
But in a match Australia had to win to regain the Ashes - a drawn series would see holders England retain the urn - Clarke opted to bat first after winning the toss despite the tourists being dismissed for just 128 in the first innings of their 347-run second Test defeat at Lord's.
Although Australia had recalled David Warner, usually an opening batsman, they stuck with all-rounder Shane Watson and left-hander Rogers as their first wicket duo.
The pair responded by putting on 76 before Watson was caught at first slip by England captain Alastair Cook for 19 off first change Tim Bresnan after James Anderson, on his Lancashire home ground, and Stuart Broad had seen several good outswingers go unrewarded.
The 35-year-old Rogers scored briskly to complete a 49-ball fifty, including 10 fours, with two successive boundaries off Anderson.
Soon afterwards, in only his fourth match at this level, Rogers surpassed his previous Test-best of 52, made in the opening match of this series at Nottingham's Trent Bridge.
But after 81 minutes Watson, as he is prone to do, pushed firmly forward and edged Bresnan to Cook.
And 76 for one became 82 for two when left-hander Khawaja, playing forward to a sharply turning delivery from off-spinner Graeme Swann, was caught behind by wicketkeeper Matt Prior for one.
Khawaja immediately reviewed on-field umpire Tony Hill's decision
Hot Spot thermal imaging did not appear to show an edge but there was a
noise on audio. After several minutes' study, third umpire Kumar
Dharmasena decided there was not enough evidence to overturn Hill's
verdict and Khawaja had to go.