Martyn, who turned 35 on Saturday, scored a solid 78 as Australia overcame a triple blow to surpass England's modest total of 169 with 13.1 overs to spare to keep alive their hopes of qualifying for the semi-finals.
Scorecard of Eng Vs Aus
Australia were reeling at 34-3 before Martyn restored their fortunes with a quality knock to ensure the superb efforts of pacemen Shane Watson (3-16) and Mitchell Johnson (3-40) did not go waste.
England are virtually out of contention after suffering their second successive defeat in the four-team Group A. They will take on the West Indies in their last league game at Ahmedabad on October 28.
India and the West Indies have one win apiece from one match, and Australia one victory from two games. The top two sides advance to the semi-finals.
Australia lost Adam Gilchrist (10), skipper Ricky Ponting (one) and Watson (21) in the space of four runs when the game resumed after a 10-minute break due to power failure.
Sajid Mahmood grabbed two wickets and fellow-paceman James Anderson one before their team ran into Martyn, who drove beautifully on both sides of the wicket to end England's early celebrations in the day-night match.
Martyn raced his 36th half-century off 35 balls with nine fours, including three in one over off key fast bowler Steve Harmison who conceded 45 runs in 4.5 overs.
The Australian middle-order batsman added 118 for the fourth wicket with Michael Hussey, who played a supporting role with an unbeaten 32.
Martyn's birthday coincided with Diwali, the country's biggest Hindu festival marked by fireworks.
There were fireworks on the field too as the Australian executed breathtaking shots during his 91-ball knock.
Australia were indebted to Watson and left-arm fast bowler Johnson for restricting England in their big clash before the Ashes, beginning at Brisbane next month.
England looked like setting a stiff target after being put in to bat when Andrew Strauss (56) and Ian Bell (43) added 83 for the opening wicket on a slow track.
Ten wickets then fell for 86 runs, with Watson and Johnson each taking three and veteran fast bowler Glenn McGrath two. McGrath conceded 27 runs in his opening four overs, but came back strongly to finish with 2-36 off nine overs.
Wicket-keeper Adam Gilchrist brilliantly supported his pacemen with five catches, including his 350th in one-day internationals.
Paul Collingwood (22 not out) and last-man Anderson (15) were the other batsmen to reach double-figures in a dismal England batting performance.
Watson provided the breakthrough with his second ball when he had make-shift opener Bell caught by Hussey in the cover. His dismissal was the beginning of the end of England's innings.
England suffered a twin setback when free-stroking batsmen Kevin Pietersen (one) and Andrew Flintoff (four) fell in quick succession to leave their team wobbling at 110-3.
Johnson had Pietersen caught by Gilchrist, while skipper Flintoff was caught pulling by Hussey at deep mid-wicket just a ball after being struck on the helmet by Watson.
Flintoff batted at two different positions in as many games, but had yet to click. He fell for a seven-ball duck against India while batting at number three. He batted at number four against Australia but lasted only 15 balls.
Australia kept striking at regular intervals to eventually neutralise England's early advantage given by Strauss and Bell.
Bell, dropped on 23 by Martyn off McGrath, hit seven fours in his 60-ball knock while Strauss struck six fours in his 12th half-century before being caught behind off spinner Andrew Symonds.