Thompson's partner, Megan Khang, had a chance to extend the playoff on Sunday, but she missed a five-foot birdie putt that was on the low side of the hole from the start.
Thompson made an eight-foot birdie putt on the par-3 18th hole, with Khang still facing a six-foot birdie attempt, as the American duo closed with a 10-under 60 in the fourballs format. They were the first to post at 20-under 260.
Lee made a 10-foot birdie putt to tie for the lead on the 17th. Im and Lee missed birdie chances on the 18th in regulation for the win.
The playoff switched to foursomes. Thompson hit the tee shot on the 18th to just five feet right of the cup. Im went nearer the pin but eight feet long, setting up Lee for the winning putt.
"Bummer to miss the last one in the playoff to force another hole, but very happy how we played," Khang said.
Thompson has not won since the ShopRite LPGA Classic in 2019 and decided last summer to no longer play a full schedule. The Dow Championship was her eighth tournament this year.
Im and Lee are in their second year on the LPGA Tour and this was their first title in America, though both were prolific winners on the Korea LPGA. Im has won six times on the KLPGA, while Lee has five KLPGA titles.
"I can't believe it," Lee said after making her winning putt.
Lindy Duncan and Miranda Wang had a 59 in the better-ball format and tied for third, two shots out of the playoff. They were joined by Manon De Roey and Pauline Roussin-Bouchard, who teamed up for a 64.
Albane Valenzuela and Sarah Schmelzel, who had the 54-hole lead, closed with a 66 and failed to make birdie over the final seven holes. They finished fifth, three shots behind.
The Dow Championship is the only official team event on the LPGA schedule.
