Poland's Hubert Hurkacz, seen as an outside tip for the Wimbledon title, was forced to quit his second-round match against Arthur Fils with a knee injury on Thursday.
It was the big-serving Pole's second Masters triumph, to go with the one he won in Miami in 2021, and a seventh ATP title in all.
Carlos Alcaraz passed a tiebreak test on Thursday as the top seed squeezed into the Toronto Masters quarter-finals with a 3-6, 7-6 (7/2), 7-6 (7/3) victory over Hubert Hurkacz
Hurkacz was pushed all the way by the Australian lucky loser Kokkinakis before emerging with a 6-7 (10/12), 7-6 (9/7), 7-6 (8/6) victory.
Korda, whose father Petr won the title in 1998, had produced one of the performances of his career to upset two-time Australian Open finalist Daniil Medvedev in the third round.
A composed Taylor Fritz downed Poland's Hubert Hurkacz in a battle of top 10 players Saturday to power the United States into the final of the inaugural United Cup, where they will meet Italy or Greece.
The Polish eighth seed managed 43 winners of his own in a rapid-fire 7-6(7/4), 6-7(5/7), 6-1 triumph that put him into his fourth semi-final at the Masters level
Pablo Carreno Busta spoiled Hubert Hurkacz's perfect record in ATP finals on Sunday, beating him 3-6, 6-3, 6-3 to win the Montreal Masters
Poland's Eighth-seeded Hurkacz needed two hours to claim a 5-7, 6-3, 6-2 victory over his Norwegian opponent
Nick Kyrgios lost 6-7 (4/7), 7-6 (7/5), 1-6 to Hubert Hurkacz in the quarter-final of the ATP Montreal Masters.