The American, the first WTA teen finalist at Washington's hardcourt event, added to a trophy haul that also included 2019 at Linz, 2021 in Parma and this past January at Auckland.
The success came after a first-round exit at Wimbledon last month.
"It was really tough a couple weeks ago," Gauff said. "We were all feeling it and I'm glad that I was able to bounce back."
World number seven Gauff, last year's French Open runner-up, had lost four of five prior matches against Sakkari, who fell to 1-7 in WTA finals with her sixth consecutive loss in a tour championship match.
"It's pretty disappointing, but a month ago we didn't think I'd be here," said the ninth-ranked Sakkari.
Gauff, who didn't drop a set all week, won the first in 42 minutes but Sakkari broke her to begin the second. They exchanged service breaks in the fourth and fifth games but Sakkari double-faulted away another break to lift Gauff level at 3-3.
Gauff held, broke in the eighth game when Sakkari swatted a forehand beyond the baseline, and held to complete the victory after 84 minutes on a backhand winner.
Sakkari won her only prior WTA title at the 2019 Morocco Open.
British ninth seed Daniel Evans and 12th-seeded Dutchman Tallon Griekspoor will meet later for the men's crown at the combined ATP-WTA tournament in Washington, a US Open tuneup event.
Evans, whose only ATP title came in a 2021 outdoor Melbourne event, is the first British finalist in Washington since Andy Murray in 2006 and hopes to be the first British champion since Tim Henman in 2003.
Griekspoor seeks his third career title after triumphs at Pune in January and 's-Hertogenbosch in June.