The Ashes holders were 209-7, still 72 runs shy of a victory target of 281, when fast bowler Cummins came in to bat after first-innings century-maker Usman Khawaja fell for a painstaking 65.
And after Alex Carey was out to leave Australia 227-8, the tourists still required another 54 more runs with Nathan Lyon the new batsman.
But the pair’s unbroken stand of 55 saw Australia home in a match to rival the tension of England’s two-run win in a celebrated 2005 Ashes clash at Edgbaston.
Cummins, who finished on 44*, hit the winning boundary when he edged Ollie Robinson to third man where a diving Harry Brook knocked the ball over the rope.
Lyon, whose missed run out contributed to England’s stunning one-wicket win at Headingley in the drawn 2019 Ashes series in England, was 16*.
Victory left Test world champions Australia 1-0 up in the five-match series as they bid for a first Ashes campaign win in England in 22 years.
This was just England’s third defeat in 14 Tests under captain Ben Stokes and coach Brendon McCullum.
HIGHLIGHTS: 2023 Ashes (1st Test, Day 5)
England were left to rue a series of missed chances throughout the match, none more so than when Lyon was dropped on just two by Stokes at square leg, after the skipper failed to hold a one-handed diving chance from a pull off Stuart Broad as he hit the turf.
After Tuesday’s morning session was washed out by rain, Australia resumed on 107-3 with veteran seamer Broad having removed Marnus Labuschagne and Steve Smith, the world’s two top-ranked Test batsmen, late on Monday’s fourth day.
But Khawaja was still there on 34* as the 36-year-old opener became only the second Australian, after Kim Hughes at Lord’s in 1980, to bat on all five days of a Test.
After nightwatchman Scott Boland fell to Broad, spinner Moeen Ali, struggling with a finger injury, struck on his Birmingham home ground.
Moeen’s first ball of the day, a rank long hop, was pulled for four by Travis Head.
But his fifth was a classic off-spinning delivery to the left-hander, taking the outside edge on its way to Joe Root at slip as a near capacity crowd erupted in celebration.
Australia reached tea at 183-5, but were quickly reduced to 192-6 when Robinson had all-rounder Cameron Green (28) chopping on to end a stand of 49 with Khawaja.
Meanwhile Stokes, capable of swinging the old ball at a lively pace, brought himself on to bowl as the floodlights came on.
Stokes struck when he had Khawaja, who made 141 in Australia’s first innings, chopping on to end a 197-ball stay.
OH MY STOKES! ?
Usman Khawaja is bowled by the captain!
Who else? ?#EnglandCricket | #Ashes pic.twitter.com/6NdZAHcbdz
— England Cricket (@englandcricket) June 20, 2023
Part-time off-spinner Root dropped two tough and caught bowled chances offered by Carey and Cummins. But he made no mistake with a third chance as he clung on to remove Carey for 20.
Cummins, however, reignited Australia’s pursuit by launching Root for two straight sixes before finishing the job himself.
© Agence France-Presse
