England's only realistic hope of avoiding defeat, having limped to 156 for five on the third evening with 420 needed for victory, lay with the weather and their prayers were answered as Sunday's first two sessions were washed out by rain.
When the fourth day finally got underway with 42 overs left, however, the home side collapsed to 180 all out without a fight.
Their last five wickets tumbled for 22 in just under eight overs, with the final four batsmen all making ducks.
Opening bowler McGrath, who claimed five wickets for two runs in an extraordinary spell in the first innings to pass 500 Test wickets, took four for 29 from 17.1 overs to complete match figures of nine for 82.
Leg spinner Shane Warne [ Images ] took four for 64 in the second innings.
"Glenn was fantastic and Warney was just great," said Australia captain Ricky Ponting [ Images ]. "Glenn's spell on day one was probably the turning point. Glenn McGrath is always turning big games."
England skipper Michael Vaughan [ Images ] said: "McGrath and Warne were outstanding and put the batsmen under a hell of a lot of pressure."
Pressure, he added, had probably also been a factor in his side dropping six catches in the game.
Kevin Pietersen [ Images ] permitted English supporters a thin smile, completing his second half-century on his debut and finishing on 64 not out.
Ponting opted to open hostilities on Sunday with McGrath at the Pavilion End and Warne, who had bamboozled the English top-order on the third day, from the Nursery.
McGrath made the breakthrough in his second over.
Two balls later it was 158 for seven as Ashley Giles drove off the back foot and edged to Matthew Hayden [ Images ] at gully.
A few more spots of rain caused another 10-minute delay but McGrath was soon back in the groove, trapping Matthew Hoggard [ Images ] lbw for another duck with a fine off-cutter.
Pietersen reached his 50 off 68 balls including a six and five fours but Steve Harmison [ Images ] went first ball to Warne without offering a stroke.
Pietersen swept Warne off middle stump for six but it was all over when Simon Jones slogged at McGrath and was caught by Warne at first slip.
"It's a sensational place to play, especially on a wicket like that," McGrath said. "When you hit the deck the slope helps my type of bowling.
"Taking 500 wickets was a special feeling, something I will always remember."
England, who lasted just 10.1 overs on Sunday, had remained in the contest for the first two days before being blown away in the third.
Australia, dismissed for 190 in their first innings, hit back through McGrath, whose five wickets for two runs secured the world champions a 35-run first-innings lead.
They took control through Michael Clarke's [ Images ] 91, the highest score of the match, and Warne's three-wicket burst on Saturday evening.
Australia have not lost at Lord's for 18 Tests, stretching back to 1934. They have won five of their last six games at the home of cricket.
The second Test of the five-match series starts at Edgbaston, Birmingham, on August 4.