The 28-year-old Japanese left-hander rallied after the showers to defeat Thompson 4-6, 7-6 (7/2), 6-2 in the first US hardcourt tuneup event for the US Open.
"This is a wonderful week for me," Nishioka said. "I got a little bit of luck after raining."
World number 86 Nishioka improved to 5-0 in career ATP matches with 41st-ranked Thompson, each win coming on hardcourts.
Nishioka, playing in his sixth career ATP final, added to a trophy haul that included the 2018 Shenzhen Open and 2022 Korea Open in Seoul.
"This is amazing feeling," Nishioka said. "Third title, I couldn't believe that from the beginning of the year."
Thompson, 30, was foiled in a bid for his second title of the year. He won his first ATP crown in February at Los Cabos, defeating Norway's Casper Ruud in the final.
"It's not the result we wanted," Thompson said. "We made the final. Not a bad week."
Nishioka will be the final winner of the Atlanta title, with the event folding after this year.
Thompson broke Nishioka for a 5-4 lead then held serve to close out the first set. Nishioka led Thompson 5-4 with the Aussie serving at 30-15 in the 10th game of the second set when rain arrived.
Showers halted the match for nearly six hours before they resumed, both players holding serve into a tie-breaker that Nishioka dominated, jumping ahead 5-0 on the way to forcing a third set.
The final set, which began just after midnight, began with Nishioka breaking for a 1-0 lead when Thompson swatted a forehand wide.
Nishioka saved a break point in the second game and three more in the fourth game, two off Thompson errors and the other off a forehand smash.
Nishioka then broke again for a 4-1 advantage by blasting a backhand cross-court winner and held twice more to claim victory after two hours and 40 minutes when Thompson sent a backhand service return long.
