Korda and Thompson got a crucial break in the fourth game and went on to win the first set. The Australian-American duo was unable to find a break in the second set but saved a crucial set point when trailing 7-6 in the tie-break.
In all, Korda and Thompson saved six break points against Behar and Pavlasek in the title decider.
Thompson and Korda defeated top-seeded Indo-Aussie pair Rohan Bopanna and Matthew Ebden in the first round before getting the better of John Peers and Andres Molteni in the second.
In the quarter-finals, Thompson and Korda accounted for Andrea Vavassori and Simone Bolelli and then staged a gritty comeback to beat Jamie Murray and Michael Venus, both former Grand Slam champions, 3-6, 6-3, 10-8 in the semi-finals.
This was Thompson’s fifth title on the ATP Tour this year. He won the ATP 250 doubles titles in Dallas, Los Cabos and Houston in addition to clinching the singles crown in Los Cabos.
In the men’s singles, Australia’s Alex de Minaur, seeded 10th, and Max Purcell failed to progress past the round of 64.
In the WTA events, Daria Saville was ousted in the round of 64 while Ellen Perez and her American partner Nicole Melichar-Martinez were knocked out in the first round of doubles.