In the tenth minute Stranraer had a great opportunity to snatch the lead but Michael Moore headed past the post from close range when he connected with a Kevin Finlayson cross with Alloa keeper James Evans left helpess.
Alloa slowly took control of the match and deserved to take the lead in the 18th minute when Iain Nicolson was on hand to fire home from two yards out following a Darran Thomson corner.
With neither side able to exert pressure to take full control of the match much of the play was in the middle of the field but Alloa extended their lead in the 68th minute when they were awarded a penalty. Graeme Brown was fouled by Derek Wingate inside the box and referee Steve Connolly had no hesitation in pointing to the spot.
Brown Ferguson stepped up and coolly slotted the ball past Michael McGovern in the Stranraer goal.
Stranraer brought on all their substitutes to try and change their fortunes but the changes made little impression and it was Alloa who extended their lead to 3-0 in the 83rd minute.
Ian Ross was perfectly placed to fire home from the edge of the penalty box when he connected with a Ross Hamilton cross.
Stranraer manager Neil Watt said at the end of the match: "Alloa deserved their victory today, we had a poor performance from my players."