A flurry of wickets threatened to undo their good work as Ireland slumped from 132-2 to 149-7.
Yet Kevin O’Brien hung around for 28 not out and Murtagh (16) clobbered some useful late runs as Ireland were all out for 207, a 122-run innings lead.
“Growing up as a kid I was dreaming of being on that honours board, just not from the away dressing room — but I guess it makes it even more special,” London-born Murtagh, who was once overlooked for England’s development squad, said.
“Even the old gits like me had a few nerves this morning. It was pretty surreal at lunch. If you’d have given us a lead of 100 on the first innings, we’d have snapped your hand off.”
England skipper Joe Root won the toss and elected to bat, handing test debutant Jason Roy and Rory Burns the chance to lay down a marker for the looming Ashes series.
Instead, a spot-on Ireland attack ruthlessly exposed the cracks in England’s batting as the hosts posted their lowest home total since scoring 77 against Australia in 1997.
Murtagh, the 37-year-old Middlesex stalwart, took lethal advantage of his local knowledge on a green-tinged Lord’s wicket and some bog-standard England batting.
When Stuart Broad walked out to bat with the hosts on 43 for seven, England had lost six wickets for seven runs.
White-ball specialist Roy, superb throughout the World Cup, had a let-off when Mark Adair had him plumb lbw off a no ball. But in Murtagh’s second over Roy (5) edged to Stirling who took a low slip catch.
Joe Denly looked assured for 23, but in the 10th over test rookie Adair shaped a ball into his pads for an lbw.
Cue an astonishing collapse.
England were bowled out in just 23.4 overs.
In 142 years of playing Test cricket, that's the quickest they've ever been bowled out at home.
Burns scratched around for six but played loosely at a full Murtagh delivery and edged behind to Gary Wilson.
With Root and Jonny Bairstow, two of the four England players to have played in the World Cup final, at the wicket an England fightback was expected. It never materialised.
Root (2) was squared up by Adair and was struck on both pads and not even a hopeful review could spare him.
Murtagh then bowled a wafting Bairstow through the gate for a duck and two balls later Chris Woakes (0) was lbw to a ball that nipped back off the seam.
Moeen Ali then edged Murtagh through to Wilson as the 37-year-old sealed his five-wicket haul.
Curran attempted a counter-attack but the carnage continued as Broad (3) edged Boyd Rankin, once an England player, behind.
Sam Curran was snaffled for 18 at short leg off Rankin to leave England on 67-9. Olly Stone struck three boundaries in an over as England surpassed the 77 runs they scored against West Indies in January but he was bowled for 19 as Adair wrapped things up.
Ireland began steadily but Curran dismissed skipper William Porterfield (14) and James McCollum (19).
Stirling and Balbirnie rode their luck but played some flashing strokes as Ireland seized control.
Stuart Broad broke the partnership on 87, trapping Stirling lbw for 36. Balbirnie, who was earlier dropped off Broad, brought up his 50 in 56 balls but became Stone’s first test victim, losing his middle stump.
Stone finished with three for 29, with Broad and Curran also taking three apiece.
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