The win revives Ukraine's hopes of reaching next year's finals in Brazil and leaves second-placed England within two points of top spot with a game in hand. Ukraine are now third just one point behind England.
Ukraine triumphed with second-half goals from Denys Garmash, Yevhen Konoplyanka, Artem Fedetskiy and substitute Roman Bezus, having been reduced to 10 men just before halftime.
Roman Zozulja was shown a straight red card for elbowing Montenegro's Vladimir Bozovic off the ball but Ukraine still took the lead through Garmash after 52 minutes.
Montenegro then had Vladimir Volkov sent off by German referee Manuel Graefe after 66 minutes and Konoplyanka added a second goal for Ukraine 11 minutes later.
Montenegro were reduced to nine men when Savo Pavicevic was dismissed in the 79th and Ukraine capitalised on their numerical advantage when Fedetskiy and substitute Bezus scored late goals to silence the City Stadium crowd.
Montenegro striker Mirko Vucinic had hit the woodwork in the first half and was twice denied by goalkeeper Andriy Pyatov before the home side had two players sent off.
Montenegro stay on 14 points from seven games ahead of England with 12 from six, while Ukraine are on 11 points from six, two points above Poland who drew 1-1 away to Moldova.
- Sports & Recreation
- Denys Garmash