The Swede (67) eagled the 18th to take the win by two strokes ahead of Spaniard Pablo Larrazabal (70) and Scot Richie Ramsay (67).
Hanson could have been forgiven if his mind was elsewhere as his one-year-old son is battling a respiratory illness in Florida.
He was granted an exemption from the ban against the use of mobile phones and only played in the tournament as his son is highly contagious, although his health is reported to be improving.
''The doctors said that when they cough, it could be just so easy for me to pick up the virus, and that's the last thing I need going to Medinah [for the Ryder Cup],'' Hanson said.
''It's just so tough as my mind is over in Florida with my wife and children.
"I'm still feeling for Tim of course, but he's getting better and better, so I'm very happy about that.
"It was especially hard yesterday, with having him in the hospital on Friday night. I didn't sleep a lot."
Hanson started the round in fifth, but only one stroke off overnight leaders Graeme Storm, Scott Jamieson, Gonzalo Fernandez-Castano and Larrazabal.
After a good start he shot back-to-back bogeys on the 13th and 14th to hand Larrazabal a two-stroke lead, but they were level again when Hanson birdied the 15th and Larrazabal bogeyed the next hole.
They were level approaching the par-five 18th, where a par for Larrazabal and that eagle from Hanson decided the contest in dramatic style.
Another automatic Ryder Cup pick Martin Kaymer shot 71 to finish tied for 21st, nine strokes off the pace, while José María Olazábal's captain's pick Nicolas Colsaerts (70) was tied for eighth, six strokes behind Hanson.
Storm, who led rounds one and two outright, signed for a 73 to finish a disappointing tied for fifth with Fernandez-Castano (73) and Henrik Stenson (69).
Alone in fourth was Jamieson (71).