Paul Heatley's chip put the leaders in front but Glenavon led 2-1 at the break thanks to a David Elebert header and close-range finish from Rhys Marshall.
Elebert completed his double before Heatley pulled one back and Jordan Owens levelled three minutes from time.
Glenavon's Kris Lindsay was dismissed before the penalty save as the Crues saw their lead cut to four points.
Lindsay was sent-off for protesting Raymond Hetherington's decision not to award a penalty for a challenge on Andy Hall when the score was 3-3.
It was part of an incident-packed encounter which saw Heatley chip keeper Jonathan Tuffey for a 14th minute opener.
Kyle Neill created both first-half goals for Glenavon - his free-kick headed in by Elebert before a corner was bundled over the line by Marshall five minutes before the break.
The outstanding Mark Skykes set up Elebert to blast in on 50 minutes but the champions produced a trademark fightback.
Heatley provided a quick response with a back-post header from Gavin Whyte's deflected cross and Owens ended a goalmouth scramble by firing home the equaliser.
There was still time for more drama, starting with the Hall penalty appeal which resulted in a red card for Lindsay.
Glenavon were then awarded a spot-kick four minutes into added time for a trip on Bradley, who had the chance to win but his straight hit was blocked by O'Neill.
"Hall's was a blatant penalty - only for decisions out of our hands we would have won," said Glenavon boss Gary Hamilton.
"The biggest disappointment was the sending off. It would not have happened had we been given the penalty.
"I am proud of the boy as we were excellent throughout and we deserved to win. We were better than Crusaders."
Crusaders keeper Sean O'Neill saved Eoin Bradley's injury-time penalty in a thrilling Mourneview Park draw.