The hosts dominated possession but Montenegro always looked dangerous on the counter-attack and they led through Dejan Damjanovic's 11th-minute goal.
Robert Lewandowski equalised for Poland five minutes later and the Poland thought they had sealed a famous win when Blaszczykowski tucked the ball into the net in stoppage time before raising his hand in celebration as he fell to his knees.
But Dutch referee Bjoern Kuipers ruled the effort out, virtually ending Poland's hopes of qualifying for next year's tournament in Brazil.
Damjanovic opened the scoring but Lewandowski soon equalised, easing past two defenders before scoring with a firm shot, his first goal for the national team in 15 months.
Montenegro lie second in Group H, level on 15 points with leaders England, who have played a game less, and one ahead of Ukraine. Poland have 10 points with three matches left.
"Poland met its match with Montenegro," Montenegro coach Branko Brnovic said. "The Poles were under a lot of pressure. They had to win to have any further chances to qualify, but they faced a very strong team.
"I am very satisfied with the performance of my team. We played without our key players, and still we showed courage and prowess."