The turning point in an evenly- contested match came shortly before half-time as the visitors' player-manager Alex Neil was sent off for deliberate handball in his penalty box.
Ryan McCord stepped up slam home what proved to be the winner from the spot, his third successful penalty of this season.
Aberdeen loanee Declan McManus missed an excellent chance on the break to finish off the ten men but Alloa held on anyway.
Celtic's League Cup conquerors Greenock Morton were brought back down to earth as Dundee came from behind to earn a deserved 3-1 win at Dens Park.
Slovakian defender Tomas Peciar headed Morton into a 23rd-minute lead, which they held until the interval.
However, Peter MacDonald equalised for John Brown's side two minutes after the restart, converting Declan Gallagher's flick-on, and MacDonald soon volleyed home a second.
Former Scotland striker Craig Beattie then sealed the points for Dundee at the second attempt in the 71st minute.
Queen of the South slipped to a surprise 2-1 defeat against Ian Murray's Dumbarton at Palmerston Park.
Chris Turner's half-volley in the 19th minute put the Sons ahead, but their lead was short-lived as seven minutes later former Dumbarton striker Iain Russell equalised with a crisp sidefooted finish. Dumbarton goalkeeper Jamie Ewings denied Russell a second with a fine second-half save before Bryan Prunty struck in the 87th minute on the rebound to snatch an unlikely triumph.
Livingston hammered Cowdenbeath 5-1 to lift themselves off the bottom. The Fife visitors took an early lead against the run of play when Nathaniel Wedderburn set up Kane Hemmings for a breakaway opener.
Two headers from Calum Fordyce swung the game in Livingston's favour, though, the second arriving on the hour mark.
Andrew Barrowman pounced to net the hosts' third before substitute Mark Burchill drilled home a fourth.
There was still time for Fordyce to complete his hat-trick, cleverly burying the ball past the irate Grant Adam in the Cowdenbeath goal.
Falkirk responded to their midweek League Cup thrashing at the hands of Aberdeen by snatching a 1-1 draw against Raith Rovers at Stark's Park.
Perhaps still suffering from Wednesday's humbling, Gary Holt's men fell behind after only two minutes as Joe Cardle teed up Grant Anderson who buried the opening goal from 15 yards.
The home side were dominant and Calum Elliot and Kevin Moon both spurned excellent chances to add to their lead in the first half.
However, after the restart Falkirk imposed themselves more on the game and were denied a leveller by a last-ditch Dougie Hill tackle when Rakish Bingham looked set to score.
Raith looked set to hold on for a valuable three points until Falkirk stole a late point courtesy of a wonderful lob by teenage substitute Kris Faulds.