Rosol, whose only ATP title came last year at Bucharest, defeated Taiwan's Lu Yen-Hsun 7-5, 4-6, 6-4 on Friday at the US Open warm-up event.
Janowicz, seeking his first ATP trophy, rallied to oust Sam Querrey 4-6, 7-5, 6-4, despite 18 aces from the American.
Janowicz, ranked 19 spots below Rosol at 52nd, reached his first Grand Slam semi-final last year at Wimbledon and last week ousted eighth-ranked Grigor Dimitrov in the second round at the Cincinnati Masters event.
Rosol, six years older than his finals rival at 29, lost to Dimitrov in this year's Bucharest final and also settled for a runner-up finish last month at Stuttgart.
Janowicz won his only prior meeting with Rosol last year at Marseille.