In piling up 313-8 at stumps, Ben Stokes (67) and Jos Buttler (47) with the key supporting roles, the home side made itself heavy favorite to make the series 2-2 at some point over the next two days. To achieve their goal of a first outright series win in England in 18 years, Australia needs to produce a chase considerably better than the 359 Stokes improbably hunted down at Headingley, though Steve Smith's presence at No. 4 makes just about anything possible.
Smith, who has 751 runs in six innings, refuses to stay out of the game and here claimed four catches at slip including one quite brilliant leaping one-hander late in the day. But Australia was far from flawless in the field, with captain Tim Paine declining to review sound lbw appeals against Denly on 54 and Buttler on 19 while Stokes survived a couple of tricky chances.
Denly had been dropped on nought late on the second evening and there was a sense of freedom to his early strokeplay, with he and Rory Burns settling in with some nerve-settling early boundaries. The introduction of Nathan Lyon only accelerated things, Denly skipping down the track twice in his first over of the day to loft the spinner back down the ground for four and six.
When Burns punched Peter Siddle down the ground it brought up the first half-century opening stand in the series by either side. Burns fell for 20 shortly afterwards, groping at a long-hop from Lyon and feathering into Paine's gloves.
Denly reached lunch on 37 from 101 balls, but captain Joe Root made an unconvincing 21 before falling 10 minutes before the break. It was an innocuous off-break from Lyon, doing little more than holding its line but pinging to slip as Root pushed forward.
From 157-2 at lunch, England added 105 runs without further loss in the middle session as Denly and Stokes took advantage of several slices of luck. Stokes offered a clear chance on 7 when he rocked back and edged a cut straight at Smith, who grassed a brisk chance at head height.
Denly secured a fourth half-century in England whites with a neat flick off the pads but had a heart-in-mouth moment soon after, Mitchell Marsh forcing one into his back pad. His appeal was passionate but it was waved away by umpire Marais Erasmus and Paine declined to review. Replays confirmed Marsh's suspicions.
Stokes might have run himself out twice had Australia managed better throws, and on 52 found himself grateful that substitute fielder Cameron Bancroft failed to pull off one of his trademark grabs at short leg.
Stokes started the evening at a bullish tempo but when he was undone by a superb Lyon delivery into off stump, all eyes were on Denly. He ticked off his previous best of 69 and took tea on 82. He got within one blow of three figures - albeit an ambitious one - but could not get there, squared up by Siddle and nicking off. The ball flicked Paine's thigh, with the wicketkeeper standing up, but did not get past Smith.
He prodded forlornly at the turf as he reluctantly left, but his efforts left the team 291 ahead. "I missed the birth of my first child - he arrived three weeks early and I was playing in Derby, the midwife said, 'Don't rush,' so I didn't," Denly said. "I hit traffic and missed it by about five minutes. So it was good to get there and see my little girl come into the world. It's been a pretty special couple of days.
"It would have been nice to get to the milestone (hundred) having worked so hard but I'd probably take it, yeah. England are in a very strong position going into day four and hopefully we get a few more runs and put them under pressure."
Proceedings sped after his dismissal, with 91 more runs and four more wickets. Jonny Bairstow, Sam Curran, and Chris Woakes came and went swiftly, the latter courtesy of Smith's stunning reactions, but Buttler's sweet timing kept England on top.
He was last out to another fine catch, from Marnus Labuschagne, leaving Jofra Archer and Jack Leach in place at the close.
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