Nordqvist sank a 4-foot putt for a bogey 5 on the soaked 18th hole while the 102nd-ranked Altomare had a six.
Course workers removed pools of standing water from the 18th green as the players approached the putting surface after their third shots. The par-4 hole had played long all afternoon and was near-treacherous for the playoff.
''I am from Sweden and I'm freezing,'' said Nordqvist, who just two months ago was confined to bed for two weeks by a bout of mononucleosis.
The 30-year-old Nordqvist earned $547,500 for the win, her first major since the 2009 LPGA Championship.
Altomare got $340,000 for only her second career top-10 finish, three weeks after the 26-year-old secured a third-place tie at the Portland Classic.
Nordqvist and Altomare both shot 66 for 9-under totals of 204. It was a 54-hole event after weather-affected play on Thursday was scrapped.
Second-round leader Moriya Jutanugarn of Thailand and two-time major winner Lydia Ko of New Zealand fell out of the playoff by dropping shots on the 18th.
Jutanugarn (72) and Ko (69) finished in a tie for third with Katherine Kirk of Australia, whose 70 included bogeys at the 16th and 17th as the chilling rain fell.
Nordqvist's victory ensured 10 different major winners in the last two seasons.
Last year, Nordqvist lost a playoff for the U.S. Women's Open after a rules violation on the second extra hole - for touching sand with her club in a fairway bunker - was relayed to her on the next hole. Brittany Lang of the U.S. won that major title.
Jutanugarn was seeking to follow her younger sister Ariya, the 2016 Women's British Open winner, as the first siblings ever to each win a women's major title.
Leading by one hole overnight, Jutanugarn reached the turn two shots ahead at 10 under after sinking a 10-foot putt for birdie at the ninth.
She lost her lead when Nordqvist surged, going five under over five holes. While the 23-year-old Thai was making bogey-6 at the 13th, Nordqvist got an eagle-3 at the 15th and a birdie at the 16th to move into sole possession of the lead at 10 under.
Nordqvist fell back on the 18th, getting a bogey-5 after pulling her tee shot into the rough. As she approached the 18th green, Altomare sank a short birdie putt at 17 to advance to 9 under.
It was soon a five-way tie for the lead when Kirk made birdie at the par-5 15th and Jutanugarn managed only par when her birdie putt rolled round the lip of the hole.