Ballymena were awarded a penalty inside the opening five minutes after Mark Haughey brought down Rutkowski.
The striker picked himself up but was unable to extend his previously flawless record from the penalty spot as Bangor keeper Deane dived to his right to push the effort away for his seventh career save from the spot.
The visitors also came close inside the opening 10 minutes as Iestyn Hughes unselfishly rolled the ball across the face of goal where the in-rushing Reece Neale could only divert the ball off the base of the post at full stretch.
The busy Neale played a through ball into the path of Jay Boyd, who took a touch inside the penalty area before his shot was blocked by the shoulder of Ballymena goalkeeper Declan Breen.
Michael Morgan volleyed an effort into the ground for Bangor with the ball bouncing up and landing on top of the Ballymena net as the visitors pressed for an opener.
Morgan had the first chance of the second period with a shot from 25 yards which Breen was able to parry behind.
Bangor were reduced to 10 men just after the hour mark when midfielder Devlin was shown a second yellow card for a clumsy challenge on Jack O'Reilly.
As Ballymena tried to make their numerical advantage count, David Toure's long range shot was palmed away at full stretch by Deane and the experienced Bangor keeper again showed his agility to divert an Aaron Jarvis snap-shot to safety as the match finished in a stalemate.