A Wayne Rooney strike after 48 minutes, an own goal from Branko Boskovic after 62 minutes, a stunning third on his debut by Andros Townsend, and an injury-time penalty from Daniel Sturridge secured England’s victory.
England lead their section with 19 points, one ahead of Ukraine and four more than Montenegro.
Montenegro appeared to set up a nervous finale when Dejan Damjanovic scored after 71 minutes but England weathered the storm and will qualify for the 2014 finals if they beat Poland at Wembley in their final qualifier on Tuesday.
The only blot on an otherwise good night for Roy Hodgson’s team was a booking for right back Kyle Walker, which will keep him out of Tuesday’s match.
Rooney opened the scoring three minutes into the second half after a 70-metre run from debutant Townsend, whose cross caused mayhem in the Montenegro defence before Rooney lashed in a left-foot shot from close range.
England doubled their lead in the 62nd minute when Branko Boskovic turned the ball into his own net after a cutback from Danny Welbeck.
Those goals settled an anxious Wembley but Montenegro proved they were not totally down and out when Manchester City’s Stevan Jovetic almost beat his club colleague Joe Hart with a 30-metre shot that smashed against Hart’s crossbar and bounced away to safety.
They did even better in the 71st minute, when Dejan Damjanovic diverted a shot from substitute Fatos Beqiraj past Hart to set England’s nerves jangling again.
But Townsend settled them in the 78th minute with a superb shot from 20 metres that swerved past Vukasin Poleksic and went in off the post.
Liverpool striker Sturridge completed the scoring from the spot in the third minute of time added on after he was fouled by Ivan Kecojevic.
(Editing by Stephen Wood)