England, set a target of 121 to win, finished on 124 for two after lunch on the third day.
Ian Bell was 65 not out on his Warwickshire home ground and Joe Root 38 not out.
This victory represented a remarkable turnaround from England’s 405-run defeat in the second Test at Lord’s, which followed their 169-run win in the first Test in Cardiff.
England put themselves in command when, after Australia captain Michael Clarke won the toss and elected to bat, they made the most of seam-friendly conditions to dismiss the tourists for just 136, with James Anderson taking an Ashes-best six for 47.
In reply, England made 281 — a first-innings lead of 145.
Australia’s second innings 265 all out then saw recalled England fast bowler Steven Finn, playing his first match at this level in two years, take a Test-best six for 79.
However, that innings also saw Anderson, England’s all-time leading Test wicket-taker suffer a side injury that ruled him out of both the remainder of this match and next week’s fourth Test at Nottingham’s Trent Bridge ground.
Australia 136 (C Rogers 52; J Anderson 6-47) and 265 (D Warner 77, P Nevill 59, M Starc 58; S Finn 6-79)
England 281 (J Root 63, M Ali 59, I Bell 53; J Hazlewood 3-74) and 124-2 (I Bell 65 no)
Result: England won by eight wickets
Series: England lead five-match series 2-1