The visitors were ahead after 12 minutes thanks to Dejan Damjanovic as Montenegro looked to maintain top spot.
They were unable to edge in front before half time, thanks to keeper Mladen Bozovic.
Poland continued to have more chances in the second half but couldn't find the crucial goal, with Blaszczykowski forcing another save out of Bosovic.
The draw means Montenegro are knocked off the top of Group H after England's win over Moldova put them ahead on goal difference.
Poland now find themselves four points behind third-placed Ukraine but have three games left to salvage their qualification hopes including a trip to Wembley.