It was a frustrating first half for Cliftonville, who were denied by the crossbar twice in the opening 30 minutes.
The first when Odhran Casey’s header from a Rory Hale corner crashed off the woodwork, before Casey was denied once again when his strong strike rattled the crossbar.
The home side grew into the half with Lewis Ridd forced to make a smart save to deny Reece Neale’s free-kick.
Bangor would break the deadlock just four minutes before the break after another free-kick from Neale was denied by Ridd.
However, this time Bangor recycled the danger through Stephen McGuinness, who played the ball back for the unmarked Owens to tap home from close range.
In the 51st minute Cliftonville levelled the game when Casey’s cross from the left flank was fired into the back of the net by Ryan Curran at the back post.
Bangor appealed that there was a foul on stopper Gareth Deane by Jonny Addis as they both battled to connect with Casey’s delivery, but referee Tim Marshall waved away the appeals.
Arthurs would give the Seasiders the lead once again with 20 minutes to go after he nodded home Jack O’Mahony’s well-timed cross.
The Reds were denied by the woodwork for a third and final time when debutant Adebayo Fapetu’s thunderous effort from 25-yards pinged off the crossbar.
With just three minutes to go, substitute Morgan rose in the box to nod Liam Burns free-kick past Ridd to put the icing on the cake of an impressive first game back for Bangor.
