Angel Cabrera (69) and Paul McGinley (70) shared second at 10-under par while Olle Karlsson (73) finished a distant fourth at minus-seven.
Stenson led by three with one round to go and played steady golf with four opening pars. He birdied five before he gave a shot back at seven, a hole he bogeyed twice this week.
The 25-year-old gave the pack a chance to come back with a double-bogey at the ninth after his second shot landed in an difficult lie in a greenside bunker.
Stenson rebounded with an impossible shot at the par-4 10th. He hit a 3-wood from the tee over the water in front of the green and landed in a bank to the right of the putting surface. Stenson decided to hit a high flop shot, then watched as the ball hit the stick and fell in for an eagle-two.
He added a birdie at No. 11 but the tournament was far from over, as Cabrera birdied Nos. 15 and 16 ahead of Stenson. When the leader bogeyed the par-5 15th after he hit into a greenside bunker, the lead was down to two.
Stenson came back with a 15-foot birdie at No. 16 to extend the lead to three, which would prove to be the winning margin.
'Im delighted to have won and it is really special to do it in such a big tournament as this,' said Stenson, who moved into the top-10 on the Order of Merit with the victory. 'I havent really given it much thought really, it will take a while to sink in, but I got the job done today and this is definitely the biggest win of my career - it will have a huge impact for me.'
Stenson won the 2000 Order of Merit on the European Challenge Tour, where he won three times. In all three victories last year, Stenson held the overnight lead heading into the final round and left with the trophy. This year in a transition to the European Tour, Stenson's previous best finish was a tie for 27th at the Portuguese Open.
'I had a really good year last year and was hoping to carry it on and get off to a good start on the main Tour but it didnt happen,' said Stenson. 'So a little while back I sat down and took a look at my game and decided I had to work hard to move onto the next level. I did that, worked really hard over the last couple of weeks, and now I feel like Ive really got it together.'
Cabrera made four birdies over his last 10 holes for a 3-under 69. The winner of the 2001 Argentina Open has now finished in the top-10 in five out six starts in the 2001 campaign.
McGinley, a co-leader with Stenson after the opening round, birdied the last two holes to earn his first top-five finish this season.
'Obviously Im disappointed not to win because I went out to win,' said McGinley. 'But to do that I had to make putts and I didnt do that so it wasnt meant to be.'
Desvonde Botes took fifth at 6-under par and Richard Green finished at minus-five for a solo sixth.
Raphael Jacquelin, Retief Goosen, David Howell, Eduardo Romero and Thomas Bjorn shared seventh at 4-under 284.
Colin Montgomerie finished tied for 12th at 3-under. Defending champion Jose Maria Olazabal, Miguel Angel Jimenez and Darren Clarke were part of a group at 1-under.
Full-field scores from the Benson and Hedges International Open