Root and Malan steadied the ship after Haseeb Hameed fell, with the visitors reaching 107-2 at tea, still trailing by 171 runs.
The duo then combined for a century partnership, pushing England's score past 200 as the sun started setting over the Brisbane skyline.
England are 220-2 at stumps, still trailing by 58 runs. Root was unbeaten on 86 with Malan 80 not out at the other end.
Root earlier set a new England record for most test runs in a calendar year, surpassing the previous best set by Ashes great Michael Vaughan in 2002.
Soon after, Root brought up his half-century, the first for an English cricketer this series. Malan followed suit later in the session.
Australia, meanwhile, were left aggrieved by the lack of Snicko technology available at the Gabba, with Malan surviving an appeal for caught behind in the afternoon session.
Josh Hazlewood believed he had found the outside edge of Malan's bat, convincing skipper Pat Cummins to call for a review — but because the third umpire did not see anything on Hotspot, the left-hander survived.
Cummins and Hazlewood were not happy with the outcome, talking with the on-field umpires after the decision was handed down.
On Thursday, it was revealed that the Snicko and front-foot no-ball technology were not available for the test due to Covid-19 complications.
