Adam Owen rescued the home side with a great goal-line clearance from an Andy Reilly strike, but minutes later Gavin Swankie delivered the cross for Kevin McMullan to lose his marker and bundle the ball over the goal-line.
Reilly came close again with a header from a Swankie delivery which was wide of the post, and Paul Watson was denied by another goal-line clearance by Jordan Smith, who managed to turn the ball over the bar from almost underneath it.
Arbroath should have had a better cushion than a single goal by the interval, but their pressure was fully rewarded in the second half.
McMullan almost doubled their lead, but was prevented from doing so by a point-blank save by Derek Jackson, and then the same player headed against the upright.
However, Arbroath scored two in two minutes from Jay Stein corners with Swankie and Robbie Raeside finding the net.
Shire's afternoon of misery was completed when another corner fron Stein was weakly punched out by Jackson to the feet of substitute Scott Taylor, who immediately drilled it back into the bottom corner of the net.