Nottingham: A terrific knock of 71 by Haddin went in vain as Australia lost by 14 runs. Anderson followed up his fifer in the first innings with five more in the second to finish with match figures of 10/162.
At lunch, Brad Haddin made an unbeaten 69 to guide Australia to 291 for nine.
Australia, chasing 311, lost three wickets to slump to 231 for nine but Haddin and number 11 James Pattinson shared an partnership of 65 to put their side on the brink of an astonishing win.
England toiled for 55 minutes without success until James Anderson removed Ashton Agar for 14, the 19-year-old edging a catch to Alastair Cook at first slip.
Anderson struck again to dismiss Mitchell Starc for one, also safely pouched by Cook.
Cook then dropped Peter Siddle off Anderson but he soon made amends to the bowler with a superb diving catch to remove the Australian fast bowler for 11.
Anderson bowled 13 overs in a row from the Radcliffe Road end before being replaced by Steven Finn and he conceded 15 runs off his first over.
Haddin reached his fifty off 115 balls, including seven fours, and Pattinson looked increasingly comfortable at the crease.
Pattinson hoisted Graeme Swann over mid-wicket for six and the pair brought up their fifty partnership off just 46 balls.
Haddin was nearly run out after being sent back by Pattinson and Finn dropped the Australian wicketkeeper when he was on 64, a very difficult chance on the backward square leg boundary.
England had taken the extra half hour with Australia nine wickets down but in an atmosphere of extreme tension the players had to leave the field with an astonishing Test match still firmly in the balance
Brief scores
England 215 (Siddle 5-50) and 375 (Bell 109, Broad 65, Pietersen 64, Cook 50)
Australia 280 (Agar 98, Hughes 81*, Smith 53, Anderson 5-85) and 296 (Haddin 71, Rogers 52, Anderson 5-73)
Result England won by 14 runs
MOM James Anderson (England)