Lee McCulloch’s second-half strike was quickly cancelled out by Liam Buchanan, his sixth goal in as many games, and Ally McCoist’s men are six points adrift of Hearts ahead of next Saturday’s trip to Tynecastle.
During a lively start at Ibrox, Gers striker Nick Law had a close-range effort ruled out for offside, while at the other end, Michael Doyle’s drive was pushed away by Steve Simonsen.
Law was again involved as Rangers spurned a decent early chance, with his pass deflecting into the path of Kris Boyd, who was unable to beat Craig McDowall.
The hosts continued to look the more likely scorers as David Templeton nodded wide before Boyd was off target with another header.
Lewis MacLeod, who was cleared to return from the Scotland squad, nearly made his mark for Rangers in the second period, unleashing a curling shot to force McDowall into a decent save.
But poor defending from Alloa was punished in the 72nd minute as a corner was allowed to reach McCulloch at the back post and he gleefully turned it home.
The relief around Ibrox was shortlived as the Wasps quickly hit back through the predatory Buchanan (78), who lashed the ball in after Simonsen was unable to hold Kevin Cawley’s shot.
Rangers appealed in vain for a penalty when Law was felled in the box in the latter stages and substitute Sebastien Faure wasted the last chance by blazing over the bar.