The Czechs, who qualified 3-0 on aggregate, were content to defend their 2-0 first-leg lead and were not really troubled until the second half when Montenegro stepped up the pressure and could have easily scored three goals.
Czech coach Michal Bilek said his team had expected Montenegro to come out strong and praised his opponents for a number of attacks in the second half that almost turned the game.
"We knew they were good on offense," Bilek told Czech television. "We deserved to qualify."
Montenegro, aiming to qualify for their first international tournament since splitting with Serbia, had a number of chances to get back into the tie.
Juventus striker Mirko Vucinic headed over the bar late in the second half and missed again minutes later when Chelsea goalkeeper Petr Cech was able to save both his shot and the rebound.
Cech, who was wearing a specially-designed mask after breaking his nose, made a number of sprawling saves including one from Dejan Damjanovic early in the second half whose shot he appeared to just nudge onto the crossbar.
Montenegro dominated the second half but Pilzen's Petr Jiracek put the game beyond reach in the 81st minute when he split two defenders and side-footed a shot that Montenegro goalkeeper Mladen Bozovic could only deflect into the net.
The Czechs, who won the European Championships in 1976, qualified for the tournament in Poland and Ukraine after finishing runners-up to Spain in group play.
