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Glenavon had taken the lead in the 28th minute through Eoin Bradley whose shot was deflected past keeper Sean O'Neill.
Crues striker Jordan Owens headed the equaliser from Michael Carvill's ball midway through the second half.
Glenavon's Bradley was then sent off after a head-to-head confrontation with home skipper Colin Coates.
Glenavon will be waiting to hear if Bradley is deemed to have been guilty of a head-butt, which would land him with an automatic six-game suspension.
After the match, Glenavon player-manager Gary Hamilton queried why his man was dismissed while Coates got a yellow card.
Bradley himself said: "Colin Coates is supposed to be one of the hard players in the Irish League, but when he goes down like that you have to wonder.
"He did his job and got me sent off."
Crusaders manager Stephen Baxter: "I didn't see the incident at all to be perfectly honest with you.
"Our boys in the dressing room are saying it was a very clean head-butt. You guys can watch it back on television and debate it.
"We should have won by five or six goals. We hit the woodwork and their keeper made some great saves.
"I thought we were awesome and Glenavon will be delighted to be going down the road with a point."
Champions Crusaders were held to a draw by Glenavon but extended their lead at the top to seven points as nearest rivals Linfield lost to Portadown.