This also marks Nagar's first Grand Slam main draw appearance.
After rain washed out first day's play, Australia, on Day 2, won the toss and opted to field. Josh Hazlewood, who replaced James Pattinson, took three wickets.
Pat Cummins also grabbed three scalps to restrict England to 258.
In reply, Australia were in trouble at 102/5 before Steve Smith's half-century revived their innings.
Smith, who was nearing a century, got injured after being struck on the neck by a fierce delivery from Jofra Archer, though returned to bat on Day 4. The 30-year-old was eventually dismissed on 92, as Australia made 250 all out - eight shy of England's first-innings total. The hosts then extended their lead to 104 by the close of play.
Smith did not return to the field at the start of the fifth day and Cricket Australia (CA) confirmed the former captain will sit out the rest of the Test because of concussion.
Rain prevented play from starting for 70 minutes (on Day 5) before Ben Stokes' century took England to 258/5d, setting the visitors a target of 267.
Archer provided England early optimism when he removed David Warner and Usman Khawaja early.
Archer had a fantastic debut, finishing with five wickets.
A half-century from Smith's replacement Marnus Labuschagne proved valuable as Australia drew the second Test and maintained their 1-0 lead.
