Britain, set an objective of 121 to win, completed on 124 for two after lunch on the third day.
Ian Chime was 65 not out on his Warwickshire home ground and Joe Root 38 not out.
This triumph spoke to an amazing turnaround from Britain's 405-run vanquish in the second Test at Lord's, which took after their 169-run win in the first Test in Cardiff.
Britain place themselves in order when, after Australia chief Michael Clarke won the hurl and chose to bat, they benefitted as much as possible from crease amicable conditions to release the vacationers for only 136, with James Anderson taking a Fiery debris best six for 47.
In answer, Britain made 281 - a first-innings lead of 145.
Australia's second innings 265 hard and fast then saw reviewed Britain quick bowler Steven Finn, playing his first match at this level in two years, take a Test-best six for 79.
On the other hand, that innings additionally saw Anderson, Britain's unsurpassed driving Test wicket-taker endure a side damage that precluded him of both the rest of this match and one week from now's fourth Test at Nottingham's Trent Extension ground. (AFP)