Bell returned to form, and first-innings centurion Root stayed in it, to ease the hosts away from early trouble second time round en route to 289 all out.
England had stumbled to 22 for two, after bowling the tourists out for 308, when Bell took guard on the back of just 56 runs in his previous nine Test attempts.
But in keeping with his team’s new brief to attack whenever feasible, he belied any personal anxiety to carry them to 170 for three at one stage.
On a sunny day which was to see 15 wickets fall, England took Australia’s last five for 44.
Yet they hit snags themselves either side of lunch, Alastair Cook spearing a catch to point off Mitchell Starc and Gary Ballance gone for a duck in the first over of the afternoon on a pitch of increasingly variable bounce – gloving Josh Hazlewood behind.
Bell and Adam Lyth responded, however, with England’s new spirit of adventure – and when the opener slog-swept Nathan Lyon for six, 50 runs had come from the first seven overs of the session.
Lyon (four for 75) got his revenge when Lyth edged an off-break to be brilliantly caught by Michael Clarke, diving one-handed to his left at slip.
But Bell oversaw a second successive half-century stand, adding 97 this time with Root and passing his own 50 when he hit Mitchell Johnson over point for his 10th four from 75 balls.
The fourth-wicket pair ended up with the same number of runs, and Ben Stokes chipped in importantly too – albeit after surviving on just five when Starc hit him in front on the back foot yet declined, along with all his team-mates, to appeal for lbw.
There was no need for an appeal to account for either Bell or Root, both bowled on the back foot – respectively when Johnson took one away off the pitch to hit middle-and-off for his first wicket of the match and then Hazlewood got one through the Yorkshireman’s defence, via his pads.
Jos Buttler joined Stokes, but not for long before he contrived to be caught behind trying to reverse-sweep Lyon.
Stokes had England’s third middle-order 50 in his sights when instead he was bowled off an inside-edge trying to drive Starc – and then Stuart Broad holed out off Lyon to a tumbling Hazlewood at long-off.
But Moeen Ali, dropped by Haddin on nought off Lyon, stayed long enough under lights to help big-hitting Mark Wood take the lead above 400.
Impressive bowling from Broad especially and James Anderson (three for 43) had made short work of the tourists’ tail before lunch.
Broad and Wood gave the opposition no leeway from the outset, rewarded with two lbw verdicts and only one run scored – and then Anderson hastened the process again with the second new ball.
Shane Watson was perhaps marginally unlucky, pushing forward at Broad and unsuccessful with DRS after Marais Erasmus had given him out – ball-tracking demonstrating a mere clip on the top of leg-stump, enough to confirm the dismissal via umpire’s call.
There was no semblance of doubt over nightwatchman Lyon’s departure, though, beaten on the crease by Wood.
It took Brad Haddin 16 balls to get off the mark, achieved on the introduction of Stokes for Broad but in unconvincing fashion with a ‘pull’ for four off an inside-edge which just missed off-stump and sped past the wicketkeeper.
Haddin followed up with two more conventional boundaries in the same Stokes over, and it was no surprise that Cook recalled Broad as soon as the new ball was taken.
It was Anderson who struck, though, finding Haddin’s outside edge on the back foot and Buttler taking a low catch to his right.
After Johnson then chipped Broad tamely to midwicket, Anderson ensured the initial three-figure lead when he had Starc edging to third slip for a duck as Australia’s last three wickets fell for just four runs.