The victory moved the Czechs level on six points with Group A leaders England, who beat them 5-0 at Wembley in their opening match and have a game in hand having played only twice.
Kosovo are third with five points after claiming their first ever win in a qualifier as they fought back to beat Bulgaria 3-2 thanks to an added time goal by substitute Elba Rashani.
The Czechs opened the scoring against Montenegro in the 18th minute when Jakub Jankto slammed a left-foot volley into the net from a tight angle after Pavel Kaderabek sent over a deep cross.
Their lead was doubled just after the break when Boris Kopitovic deflected Patrik Schick's cross into his own goal after the forward had rounded a defender.
Schick got the third with a penalty in the 82nd which he smashed home after being sent sprawling in the area.
Montenegro -- who fired Serbian coach Ljubisa Tumbakovic on Saturday after he pulled out of Friday's qualifier against Kosovo which they drew 1-1 -- have two points.
(Reporting by Michael Kahn; Editing by Ken Ferris)
