Australia had dragged the game back from the brink with their second match-changing 10th wicket stand of the Test, but after lunch Anderson resumed and struck the crucial blow as he removed Brad Haddin for a gutsy 71.
Haddin drove at the ball, and England reviewed for a possible nick after Umpire Aleem Dar had ruled it was not out. Hot Spot showed a faint inside-edge, consistent with the sound as ball passed bat, and third umpire Marais Erasmus correctly overturned the original call.
"He played really well, and showed his experience," said Australia captain Michael Clarke of Haddin's valiant effort. "The boys can hold their head high, it was a wonderful game of cricket. The two best performers were Ian Bell and James Anderson so they [England] deserved to win."
It was only fitting Anderson claimed the scalp - by some distance he was the stand-out bowler, taking five wickets in each innings.
It sparked a collective sigh of relief from the England supporters: time and again the hosts forged match-winning positions, only to contrive to give them away.
"I always said I would be the only England captain not to go bald," joked England skipper Alastair Cook after the game.
"Jimmy was outstanding - he always wants one more over. He's a world-class bowler, and he had amazing rhythm today."
On Bell, Cook added: "It was a real innings of character on a slow wicket."
Having clinched a 1-0 lead, England are in control of the five-match series ahead of the second game, which begins at Lord's on Thursday.
THE LUNCH REPORT
Australia (280 and 291-9 from 108 overs: Haddin 69*, Rogers 52) trail England (215 and 375) by 20 runs.
Brad Haddin and James Pattinson threatened to pull off a heist to win Australia the first Test at Trent Bridge.
The last-wicket stand added 60 runs of the 80 they required for victory before lunch had to be taken, half an hour later than scheduled.
It appeared that James Anderson’s three wickets in an another masterful spell had finally broken Australia’s resistance, but Haddin (69 not out), and Pattinson (unbeaten on 22) gave Australia hope once more.
It is one of cricket's foibles that with the game so close to resolution the players took to the pavilion for a 40-minute interval, but it gave the crowd in Nottingham a chance to draw breath after two-and-a-half exhilarating and nerve-wracking hours.
The match has echoed closely the 2005 Edgbaston Test match, in which a desperate last stand from Australia almost stole victory from England's grasp, only for Steve Harmison to get the wicket of Michael Kasprowicz and seal a two-run win.
The leader of the hosts’ attack was inspired, teasing unsuccessfully with the reversing old ball, and then striking decisively with the new one, prising out three wickets.
But once again in this match, having done the majority of the work, the 10th-wicket stand saw England unravel.
It had been a testing, tense opening hour for England, as Haddin and Ashton Agar survived rather than thrived on a slow pitch.
With the crowd subdued and nervous, it was a thrilling passage of play. Graeme Swann and Stuart Broad probed along with Anderson; Australia met their challenge with the same determination that has typified this thrilling Test.
Agar, fluent and carefree in the first innings, was stoic and defiant in the second. But when Anderson got a ball to swing away from him from around the wicket, the new ball flew to Alastair Cook at slip.
Anderson’s run around the outfield in delight and the roars of the Trent Bridge crowd reflected the importance of the breakthrough – Australia had inched to within 104 runs of victory.
Wickets have fallen in clusters all through the Test, and Anderson bagged another in his next over, with Cook again grabbing on as Mitchell Starc pushed at a tricky delivery.
Peter Siddle was gifted a second chance when Cook missed an edge at slip, but at the second time of asking he took a sensational catch – at full stretch and with two hands, the England skipper flew to his right and ended Siddle’s innings on 11.
Haddin ploughed on, but his scoring opportunities were limited. He took to driving uppishly and edgily into the off-side to keep the scoreboard ticking over, and was lucky not to lose his wicket when Swann managed to turn two balls through the gap between his bat and pad in the same over.
But suddenly, with Steven Finn's fragile confidence exposed in two costly overs, Haddin kicked into gear and the chase was back on.
It was unfortunate, but perhaps unsurprising, that Finn was the man to drop Haddin in the deep as he swept Swann.
With Haddin on 64, and Australia 28 runs shy, Finn made the ground, only for the ball to slip through his hands. Did the Test slip away from England with it?
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- Brad Haddin