Croatian Coric crashed out in Toronto in the first round earlier this month but produced a pristine performance in Cincinnati with few unforced errors, wrapping up the match that began on Monday but was suspended due to bad weather.
Korda, who has suffered a handful of early exits since reaching the Queen's Club semi-finals, appeared to have the edge as he converted a breakpoint in the third game.
But 15th seed Coric levelled in the sixth and mounted a fine defence to rally from a 4-1 deficit in the tiebreak.
He won the critical break point in the third game of the second set, where he dropped only one first-serve point as Korda's level declined across the board, and pumped his fist as he closed the affair with an unreturnable serve.
Coric next faces either Australian Thanasi Kokkinakis or Poland's Hubert Hurkacz, who were set to play later on Tuesday.
Earlier on Tuesday, top American Fritz mustered all of his resources in an epic 30-point first-set tiebreak with Lehecka.
The Monte Carlo semi-finalist saved five set points in the tense and closely fought first set, where he produced fewer unforced errors to get the upper hand.
The momentum belonged to Fritz in the second set, though, when he never faced a break point and won all but one of his first-serve points.
