The opener came after just five minutes and was the fault of home keeper Anton Nugent, who completely misjudged a corner by Jay Stein which gave Bryan Scott a free header.
The keeper later redeemed himself somewhat with two great saves to deny Barry Sellars and Bryan Scott to keep his side in contention.
The home team had chances to pull level before the break with Marc McKenzie and Paul Tweedie rattling the woodwork with Arbroath's Mark Peat well beaten.
Arbroath went close again straight after the break when a slip by centre back Gary Wild left Scott with the home goal at his mercy. This time the woodwork came to Shire's rescue as the striker's finish rebounded off the post, and Shire escaped further punishment when Sellars drove the rebound wide of the goal.
The visitors doulbled their advantage when man-of- the-match Scott broke down the left to tee up Willie Martin, whose low drive from the edge of the box found the far corner of the net, despite Nugent's despairing dive.
The keeper stopped Shire falling further behind by diving at Willie Martin's feet to concede a corner after Scott had once again set up the danger inside the box.
Shire kept plugging away right to the end, but Arbroath were never in danger of conceding a goal.