The visitors dominated the first half and Joe Savage came close to putting them ahead with an effort which cannoned off the bar but they had to wait until five minutes before the interval before taking the lead.
A Scott Chaplain shot was blocked on the line by Jamie Bishop who was sent off for deliberately handling the ball. Ciaran Donnelly confidently converted the resultant penalty.
Arbroath came out for the second half with all guns blazing and grabbed a deserved equaliser in the 50th minute. Robbie Raeside latched on to a Steven Rennie free-kick and shot low into the net from 15 yards.
Rovers were, however, back in front within 60 seconds. Ian Dobbins fouled Savage on the edge of the penalty box and Jamie Doyle expertly lofted the free-kick high into the net via Mark Peat's right-hand post.
The home side showed tremendous character to fight back and within three minutes they were level again, Barry Sellars firing an 18-yard free kick beyond the reach of Jamie Ewings.
Arbroath then pressed for a winner but were caught out by an Albion counter-attack which ended with substitute Pat Walker slotting the ball home after being left unmarked in the box.
Arbroath refused to give up however and substitute Bryan Scott almost equalised for a third time with a rising shot which Ewings tipped on to the bar.
Scott again came close in the dying seconds with a low effort which Ewings smothered.