England lost the wicket of Peter Nevill in the first hour of day three, but made steady progress.
Steven Finn had Nevill caught behind for 59, as Australia moved to 81 runs ahead, which won't worry England too much.
Mitchell Starc is still at the crease on 36 non out.
England fast bowler Jimmy Anderson has been ruled out of the Fourth Test at Trent Bridge, the ECB have confirmed. Lancastrian Anderson suffered a side strain on Thursday forcing him to leave the field of play mid-over.
England are on the brink of a 2-1 Ashes lead at Edgbaston, but already appear to be bracing themselves for James Anderson's absence from next week's fourth Test.
Anderson had to leave the field mid-over on day two in Birmingham, wincing in pain with an injury England later described as a "tight side".
Steven Finn had much to do with England's surge towards a mid-series advantage, taking five for 45 to push his match tally up to seven wickets in his comeback Test after two years out of the team.
But even as he reflected on that heartening success so far, Finn admitted concerns that Anderson - who took six first-innings wickets here - may not be fit to take part on his happiest hunting ground of all in Nottingham next week.
For Jimmy to walk off halfway through an over, it can't be too good. But who knows - with some magical medical healing and some rehab, you never know.
Jimmy loves bowling at Trent Bridge - everyone knows that. If he was to miss it, it would be a big loss - but we don't know yet.
Steven Finn clean bowled Mitchell Marsh to leave Australia on 92-5, still 53 behind England.
The Middlesex paceman now has four wickets in the second innings, making it an impressive return to Test cricket after a two-year absence.
A couple have got engaged this lunch time at the Ashes, which are being held at the Edgbaston cricket grounds.
England took a lead 85 into lunch thanks to some good batting from Joe Root, but Australia will feel they had the better of the morning session.
Mitchell Johnson got two wickets early on, while Mitchell Starc and Nathan Lyon took one apiece.
Moeen Ali and Stuart Broad were the two not out batsmen for the hosts, as they reached 221-7.
Mitchell Johnson earned the wickets of Jonny Bairstow and Ben Stokes early on day two.
The Australian bowled two superb bouncers, which the Englishmen found unplayable.
Joe Root made 63 before Mitchell Starc had him caught at first slip by Adam Voges.
Following their departure from the crease, Root and Jos Buttler dug in to progress the innings to 182-6.
England took control of the Third Test at Edgbaston by dismissing Australia for just 136 in less than 37 overs on day one.
Jimmy Anderson picked up six wickets, as the tourists struggled with the Lancastrian's swing.
Only Chris Rogers came out of the innings with any credit with the bat, hitting 52 before being trapped LBW by Stuart Broad.
Jimmy Anderson has five wickets to his name, leaving Australia on 99-7 when rain stopped play just before 3pm.
Jimmy Anderson removed Adam Voges, Mitchell Marsh and Peter Nevill in quick succession to leave Australia on 86-6 on day one in Birmingham.
Nevill was Anderson's fourth wicket when the Lancastrian struck his off-stump after the Australian left the ball.