Falkirk leapfrogged two positions in the league to their highest SPFL Championship spot with these three points.
Goals from captain Jordan McGhee and Mark Waddington - his first as a pro - gave the Bairns the win and the lift.
Partick Thistle now occupy bottom spot in the SPFL Championship and were playing in the William Hill Scottiwsh Cup while the hosts Alloa slipped to ninth.
The Wasps were far from the pushovers the expectant Falkirk support thought they might be and had the better of the first half.
They did though have to come from behind, when Jordan McGhee's floated header sailed into Neil Parry's top corner from Zak Rudden's cross. The Lithuanian had himself been tempted to try an overhead kick but moved wide before suopplying the opener.
LEAGUE TABLE: SPFL Championship
The Bairns defence though had been hard-wroked. Dario Zannatta in particular was giving Ciaran McKenna and McGhee a busy time and the Wasps funnelled much of their play down their own left side.
It was from that wing the leveller came when Zannatta out-paced McKenna into the corner and crossed for Connor Shields' well-timed run and the forward slammed into the net at the front-post to level matters with 15 minutes of the half still to go.
It was however a fairly uneventful spell, until injury time when William Edjenguele sliced a low cross backwards and would have beaten Harry Burgoyne but for Ciaran McKenna's clearance on line.
Ray McKinnon had kept his distance in the dugout, leaving Darren Taylor to holler the instructions from the edge of the technical area. Whatever was said in the dressing room at the interval, worked a treat.
AS IT HAPPENED: Alloa 1 Falkirk 2 live blog
The Bairns had began the game well but Alloa's tidy play was more than a match, but the visitors burst into the lead again just two minutes after the restart when Petravicius' low cross on the left found it's way through to Mark Waddington unmarked at the backpost and he tucked it in.
The good times continued for much of the second half. The Bairns contingent, which made up three quarters of the Indodrill Stadium's crowd, roared with every Bairns attack then, and wanted a penalty when Ross MacLean srang into the box but stood on the ball in the 75th minute.
Craig Thomson had a good view of it, and made the right call, but Zak Rudden went down seconds later and prompted an angry reaction from his man-marker, Sam Roscoe. The pair squared up behind the referee's back before the whistler called both in and cautioned both - the first cards of the match, with 15 minutes to go.
Rudden was removed with seven minutes to go, replaced by Nikolay Todorov and left to the fans singing his name - despite a second game not scoring. That could probaboly be considered a goalscoring drought for the prolific on-loan Rangers man.
Falkirk had chances late on to add to the scoreline, but Paul Paton saw an attempt fly wide and Ross MacLean blazed over in a carbon copy of Waddington's winner.
MacLean was unlucky when he beat Parry in a footrace and clipped towards goal, but Roscoe's retreating run and slide managed to divert the ball out for a corner.
In injury time Alloa goalkeeper Neil parry made a charge up field to help attack a corner but Falkirk number one Harry Burgoyne kept the ball out under pressure and Craig Thomson followed with the whistle.
Falkirk now have two weeks to wait before hosting Dundee United at The Falkirk Stadium with next week's intended opponents, Ross County, involved in the semi-final of the Irn-Bru Cup on Friday.