Totally in charge before the break after Wayne Rooney's sixth-minute headed goal, Roy Hodgson's side were under siege in the second half and Dejan Damjanovic's 77th-minute leveller produced wild celebrations in the City Stadium.
Favourites England are yet to beat any of the serious contenders in a group which also contains Poland and Ukraine and must make up a two-point gap on Montenegro who continue to punch well above their weight.
With England's qualification campaign now on hold until September, Montenegro, who have 14 points, can stretch their lead to five points if they beat Ukraine at home in June.
"It was a big point for us," Montenegro's Stefan Savic told ITV Sport. "We were a bit afraid early on but we came back and we deserved a point."
England manager Roy Hodgson talked up the result but the reality is his side's only wins have come against San Marino twice and Moldova and they are struggling to put together a consistent 90 minutes.
"Our first half was very good but we didn't start the second half as we liked and that gave Montenegro some encouragement but I thought we hung on well and finished strongly," he told ITV.
"A draw here gives us a chance for the future."
England captain Steven Gerrard was more scathing of a second-half meltdown that turned what looked like a straightforward win into a damaging draw.
"We stopped playing and away from home you can't afford to do that," said Gerrard, who nearly earned his side a dramatic late win with a free kick.
"We stopped passing and they got a deserved equaliser. They took control in the second half apart from the last 10 minutes."
Fourth-ranked England are yet to beat Montenegro, a country with a population of 700,000, in three competitive matches after drawing twice on the way to reaching Euro 2012.
That looked about to change as the visitors, buoyed by an 8-0 hammering of San Marino on Friday, took full advantage of a nervy start by the hosts.
Rooney, looking to make amends after being red-carded when England drew 2-2 in Podgorica in the Euro 2012 qualifying campaign, terrorised a lumbering Montenegro defence early on and struck the post with a delicate lob.
Glen Johnson then forced a great save from keeper Mladen Bozovic before Rooney opened the scoring.
Gerrard's perfect inswinging delivery from a corner found Rooney unmarked and he buried a downward header past Bozovic for his 35th international goal.
Montenegro's dangermen Mirko Vucinic and Stevan Jovetic were almost invisible as England threatened with every attack.
Rooney just failed to wrap his foot around James Milner's driven cross and he crossed for United team-mate Danny Welbeck who could not quite stretch his neck to head in.
Welbeck was booked for simulation when he fell in the area although television replays suggested he had been clipped by Stefan Savic.
Montenegro needed a spark and they got it early in the second half when skipper Vucinic rose to head a corner into the side-netting, the Juventus frontman turning to the crowd immediately to raise the decibel level.
England were suddenly in full retreat after such a composed opening period. Marko Basa went close with a header and Vucinic wasted Montenegro's best chance when he side-footed over the crossbar after a panicky clearance from Joleon Lescott.
Vucinic was causing all sorts of problems for England, who could not string two passes together, and curled an effort narrowly wide with 20 minutes remaining as the visitors hung on.
Hart clawed away a goalbound Jovetic effort and Montenegro were denied by the post after a scramble in the area.
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