Han birdied the final two holes of regulation to close a 4-under 68 to join Lee at 15-under-par 273. Lee birdied the 16th and 17th holes en route to a 6-under 66 at Corning Country Club.
Lee left herself 60 feet and managed to two putt for par from there. Han had a look at an 18-footer, but was unable to sink the birdie try.
Back at the 18th, Lee had a tough lie in the right rough, but managed to advance the ball near the green. She then pitched to 15 feet. Han could only two putt for par from 30 feet, then Lee drained the clutch 15-foot par save to extend the playoff.
They shifted back to the eighth for the fourth extra hole. Lee knocked her second shot over the green and left herself 18 feet for par. She missed that putt setting Han up for the win.
Han's 8-iron approach shot stopped 15 feet from the hole. After Lee missed her par putt, Han two-putted for par and her fifth tour win.
'I was pretty nervous out there,' admitted Han, who collected $180,000 for the win. 'Meena played with me a couple of times, and she's pretty good. I was just thinking keep it in the fairways and greens in the playoff. The greens were especially tough today. I got a little lucky on 18 and eight. I hit the trees and they both went in the fairway.'
Brandie Burton took third place at 14-under-par after a 2-under 70. Mhairi McKay was one stroke further back at minus-13 thanks to a final-round 68. Laura Diaz (70) and second-round leader Virada Nirapathpongporn (72) shared fifth place at 12-under-par 276.
Reigning Women's British Open champion and third-round leader Jeong Jang struggled to a 4-over 76 to end in a tie for seventh at minus-11.
Han opened her round with a two-putt birdie on No. 5 to move to 12 under. Her tee shot at the seventh stopped 3 feet from the cup and she kicked that in for birdie.
The 27-year-old missed the next two greens and tripped to bogeys on both holes to slide back to 11 under. Han got one of those strokes back with a 3-foot birdie on 12, and was back to 13 under when she sank a 10-foot birdie try at the 14th.
Han converted a 25-foot birdie putt at the 17th to get within one off Lee's lead. Han then stuck her 8-iron approach within 3 feet at the last to force the playoff.
Lee birdied the second to move to 10 under at the start of her round. She then two-putted from 36 feet for birdie on the par-5 fifth.
The 24-year-old nearly holed her tee shot at the par-3 seventh, but settled for a tap-in birdie from a foot. Lee ran home a 60-foot birdie effort at ninth to turn at 13 under.
Lee knocked her third to a foot at the par-5 12th for birdie. She missed the green at 13 and bogeyed that to slip to 13 under. Lee birdied 16 and 17 to get to 15-under and watched as Han, playing four groups behind her, caught up with her late birdies.
'I'm satisfied with what I have done and how I played today, the one thing I'm not happy with is that I didn't win,' Lee said. 'I never thought about winning. I just didn't think of that at all. I'm satisfied with how I played today. It's just that I think I made one big mistake on the playoff.'
Jang was joined in seventh place by Natalie Gulbis, Morgan Pressel, Reilley Rankin, Nancy Scranton and Giulia Sergas. Mi Hyun Kim, Tina Barrett and Audra Burks were one stroke further back at minus-10.