The Red Lichties dominated the opening period and deservedly went ahead in the 23rd minute but were dealt a serious blow on the stroke of half-time when Roddy Black, who had been booked earlier, was sent off for a late tackle on Jamie Stevenson.
Arbroath created the first chance after five minutes when Andy Reilly's cross was met by Gavin Swankie but Allan Creer brilliantly tipped the ball behind for a corner.
But Alloa hit back and Arbroath keeper Neil Inglis did well to beat away a goalbound Brian McColligan drive from 20 yards.
Jamie Stevenson then came close in the 22nd minute with a 25-yard free-kick which Inglis pushed behind.
Sixty seconds later Arbroath went ahead through Reilly. The little striker took possession wide on the right, waltzed past two defenders and fired powerfully into the net from 12 yards.
Arbroath continued to press and had a strong penalty claim turned down when Swankie tumbled under a Michael Bolochoweckyj challenge.
The first half ended in controversy with Black's dismissal and the visitors equalised eight minutes after the break when Robert Sloan outpaced the Arbroath defence and slotted the ball beyond Inglis for his tenth goal of the season.
Arbroath fought back and an Ian Dobbins header was well saved by Creer, then Swankie shot narrowly over.
Alloa failed to take full advantage of the extra man and created very few chances. Indeed Arbroath almost snatched victory in the final minute when Swankie's overhead kick was scrambled off the line by Chris Townsley.