Hansen was among 14 players who became exempt from U.S. Open qualifying by being in the top 50 in the world ranking or the top 10 on the current PGA TOUR money list.
The U.S. Open is to be played June 14-17 at Oakmont. The 36-hole qualifying will be held next week.
It was the first victory for the 36-year-old Dane since he won at Wentworth five years ago. Hansen birdied the 18th hole in regulation, then made a 25-foot birdie putt to beat Justin Rose on the first extra hole. Angel Cabrera finished two shots out of the playoff at Wentworth, and his tie for fifth moved him up 15 spots in the ranking to No. 39.
On the PGA TOUR, Tim Clark birdied three of his last six holes at Colonial to tie for 12th, but it gave him just enough world ranking points to move up three spots to No. 50 and avoid having to go through 36-hole qualifying.
John Rollins qualified by being among the top 10 on the PGA TOUR money list. The others who qualified by being in the top 50 in the world ranking were Rose, Charles Howell III, Robert Allenby, Aaron Baddeley, Jose Maria Olazabal, Scott Verplank, Chris DiMarco, Vaughn Taylor, Lee Westwood and Charl Schwartzel.
All of them had been inside the top 50 going into last week.