their victory target of 311 and all but out of the match.
England's Jonathan Trott (C) celebrates England's narrow victory over Australia on the fifth day of the first Ashes Test match at Trent Bridge. (AFP Photo)
But by lunch they were 291 for nine, just 20 runs away from a stunning upset with Brad Haddin 69 not out and James Pattinson unbeaten on 22.
However, the third over after lunch saw Haddin, on 71, eventually given out caught behind by opposing wicketkeeper Matt Prior off man-of-the-match Anderson's full-length delivery
England, in a Test full of controversial umpiring decisions, had though first to challenge Pakistani on-field umpire Aleem Dar's original not out verdict.
But third umpire Marais Erasmus, using Hot Spot technology, overturned the call and that meant Ashes-holders England had gone 1-0 up in this five-match series ahead of the second Test at Lord's on Thursday.
Pattinson finished on 25 not out after a last-wicket stand of 65.
It was the second remarkable last-wicket Australia partnership of the match after their first innings 163, a tenth wicket Test record featuring teenage debutant Ashton Agar's 98 - the highest score by a Test No 11.
England spearhead seamer Anderson, who took four wickets for 12 runs Sunday, finished with an innings return of five for 73 and a match haul of 10 for 158 - only the second time in his 83-Test career he'd taken 10 or more in a Test following his 11 for 71 against Pakistan at Trent Bridge in 2010.
Credit to Anderson
"Australia battled hard and a lot of credit to them. Jimmy was outstanding," said England captain Alastair Cook at the presentation ceremony.
Meanwhile, Australia captain Michael Clarke said Anderson and England batsman Ian Bell, whose second innings 109 laid the platform for victory, had been the difference between the sides.
"The boys can hold their heads high," said Clarke, after Australia's fifth straight Test loss, in their first Test under new coach Darren Lehmann, following their 4-0 thrashing in India earlier this year
"It was a wonderful game of cricket but credit to England, they fought well. The two best performers in the match were Ian Bell and Jimmy Anderson and England deserved the win."
Anderson, who has now taken 49 wickets in seven Trent Bridge Tests at just over 17 apiece, admitted: "The match had the nerves going but I love bowling here and I'm happy to pick up some wickets again.
"It generally swings here but whatever way we can get the ball moving, it is a bonus for us."
All was going well for England earlier Sunday when Anderson took three wickets for six runs as Agar (14), Mitchell Starc (one) and Peter Siddle (11) were all caught by Cook at first slip to leave Australia nine down.
But when Pattinson swept off-spinner Graeme Swann for six, Australia needed just 31 more runs for victory.
Haddin, with 26 needed, was dropped on 64 by a diving Steven Finn, running round in the deep, off Swann as a sun-drenched capacity crowd of 17,000 watched the most nerve-jangling climax to an Ashes Test since England's two-run win at Edgbaston in 2005.
Dar, Erasmus to stay
Match officials Marais Erasmus and Aleem Dar will not be forced to step down from umpiring the Ashes series despite their bungling of the decisions over England's Stuart Broad and Jonathan Trott, which overshadowed the Ashes opener.