Hensby and Stenson both fired 6-under 65s in the final round to end the tournament at 22-under-par 262, three strokes clear of Marc Cayeux and overnight co-leader Bradley Dredge.
Stenson held the clubhouse lead at minus-22 after an eagle at the par-5 17th and an up-an-down par from a bunker at the 18th. But Hensby -- playing in the final group with Dredge and Barry Lane, the other overnight co-leader -- followed by collecting birdies on his final two holes.
He drained a huge putt at No. 18 to force the playoff.
'Sometimes it's easy to make a putt when you've only got one option, and my one option was to hole it to get into a playoff,' said Hensby. 'I just thought, 'get up and hit a solid putt and see where it goes.''
The players parred their first playoff hole before heading back to No. 18 for the second, where they each landed safely in the fairway off the tee.
Stenson then pushed his second shot to the right side of the green, while Hensby dropped his short, but within 15 feet.
Looking at a long putt for birdie, Stenson missed the hole well-left and long, leaving the Swede with a little work for par. Hensby, on the other hand, came up just short and had an easy tap-in for his par.
That left Stenson with a knee-knocker, which he pulled left to give Hensby the win.
Hensby, who finished tied for third place at last month's U.S. Open, picked up his first win on the European Tour and earned a two-year exemption. He is the first Australian ever to win this event, and the victory has him looking for more.
'Now that I've won, I think I can come over here (Europe) and play a little bit more, which I really want to do,' said Hensby. 'You get so used to the same faces, and I love the American tour, but now I'm definitely going to spend a bit more time over here.'
Hensby played the final four Kungsangen holes at 11 under for the tournament, so his late charge to tie Stenson wasn't surprising.
'The back-nine was good to me this week, no doubt,' Hensby said.
Hensby and Stenson both fired 7-under 64s in the third round to enter Sunday tied for second place behind Dredge and Lane.
Stenson reached 19 under par around the turn after mixing four birdies with one bogey on the front nine. He collected another birdie at No. 10 and parred six straight holes before his eagle on 17.
Hensby played 1 under over the front nine after a birdies at Nos. 5 and 9 and a bogey at the seventh. But he played the back-nine at 5 under, collecting birdies at 10, 13, 15, 17 and 18.
Cayeux also fired a 65 Sunday thanks to birdies on seven of his last nine holes. Dredge shot a 1-under 70 for a share of third place after posting a 5-under 66 Saturday to share the lead.
Pierre Fulke and Adam Scott tied for fifth place at 16-under-par 268 after both shot 3-under 68s in the final round. Lane struggled to a 3-over 74 to fall into a seventh-place tie with three other golfers at 15-under-par 269.