McGrath, back after a one-year injury lay-off, and Shane Warne polished off the Sri Lankans before Australia were bowled out in their second innings for 201 in a low-scoring match where 30 wickets have fallen in two days.
McGrath took five for 37 off 15 overs while Warne's three tailenders for 20 took him to 520 Test wickets, seven behind world record holder Muttiah Muralitharan.
Sri Lanka began the day at 43 for three, 164 runs adrift but still in the match. By lunch, however, they were in serious trouble as they lost their last seven wickets for 54.
The 34-year-old McGrath moved to fourth on the all-time list of Test wicket-takers with 435 in 96 matches, surpassing Richard Hadlee of New Zealand and India's Kapil Dev.
McGrath was playing his first Test after ankle surgery and the fast bowler made good use of a seaming pitch at Darwin's Marrara Oval in Australia's tropical north.
He had Thilan Samaraweera (1) and Nuwan Zoysa (12) caught behind and when Matthew Elliott held on at second slip to remove Russel Arnold (6), McGrath had claimed his 24th five-wicket haul.
Leg spinner Warne then removed the tail.
The highlight of Australia's second innings was Adam Gilchrist's 80 before he became the ninth wicket to fall, run out in the penultimate over of the day.
Darren Lehmann, who top-scored in the first innings with 57, also played another key role with 51 from 59 deliveries.
Until their contribution, the home side looked in danger of a wretched score themselves.
Justin Langer went for 10, Matthew Hayden for two and Matthew Elliott for a three-ball duck as they slid to 14 for three.
Lehmann, however, relaunced the innings before departing caught behind to debutant paceman Lasith Malinga, who took four for 42 with his explosive, slingy action. Wicketkeeper Kumar Sangakkara took four catches during the second innings.
Stand-in captain Gilchrist came to the crease with Australia on 77 for five and they slipped to 127 for seven before he combined with the tailenders to add another 74.
