England were forced to share a point with Montenegro, putting them two points adrift of the Group H leaders, following a second-half surge from the home side.
The Three Lions started the stronger side and could have broken the deadlock after three minutes when Wayne Rooney tried a chip, which fell a width wide of the post.
Minutes later, Rooney was able to hand England the lead courtesy of a whipping ball from Steven Gerrard from the corner, which allowed the frontman to meet the ball with his head and hammer it into the back of the net.
Following a tentative spell, the Three Lions began to take control of the fixture with Gerrard, who attempted a shot on goal, but it was blocked by Montenegro's defence.
The home side were able to throw a number of passes together towards the closing stages of the first half, which resulted in a 35-yard shot from Zverotic, which was blocked by Joleon Lescott.
Montenegro came out pressing in the second 45 minutes, and their early work almost paid off following an attack down the right-hand side through Stefan Savic, who crossed deep into the area to find the head of Stevan Jovetic, who glided his effort wide of the near post.
Minutes later, the home nation had another chance to find the back of the net through Marko Basa. Vukcevic whipped in a corner to find the head of Basa, but his effort ended up on the wrong side of the post for Montenegro.
At the other end, England had the chance to double their lead with a free kick on the edge of the area after Danny Welbeck was brought down. Rooney stepped up to take it, but it was saved by Bozovic with ease.
England were unable to hold off any more pressure from their opponents when goalkeeper Joe Hart was beaten after three swift attempts by half-time substitute Dejan Damjanovic, who tapped the ball into the back of the net following a deflection from Hart.
The Three Lions are now two points adrift of leaders Montenego in Group H.