Inverness took advantage of Ayr being idle because of a frozen pitch to leapfrog them into second place in the Championship, albeit having played two games more.
Caley boss John Robertson said: “It was one of the best games to watch I’ve seen in a long time. The first goal was a bit of a fluke, but the second was a terrific finish by Aaron Doran. We defended well when we had to. The annoying thing is we didn’t show enough care in the final third.
“Our problem this season is we have not put a run together to get ourselves back in there. In this league it is foolish to look too far forward.”
Inverness, unbeaten in their last six clashes with the Wasps for over three years, almost went behind after three minutes when Kevin Cawley and Kevin O’Hara combined to set up Alan Trouten, but the striker, sliding in at the back post, put the ball wide.
The shot-shy visitors, with just one goal in their previous four games, should have taken the lead after 15 minutes when James Keatings floated the ball in from the right for the unmarked Carl Tremarco, who timed his run to perfection. But the Caley captain somehow headed off target.
Peter Grant’s part-time outfit, unbeaten in their previous three games, responded well and after 25 minutes Iain Flannigan cut on his right foot to fire in a curling 20 yard effort which goalkeeper Mark Ridgers did superbly well to turn over.
The deadlock was finally broken three minutes later when a long clearance from Donaldson was headed past goalkeeper MacDonald into his own net by Scott Taggart to give Caley the lead.
Caley got the decisive second right on the interval when Storey clipped the ball on to Jordan White for Doran to blast a superb ball high into the net from 18 yards.
Worse was to follow for the Wasps when they were reduced to ten men on the hour mark when Liam Dick was shown a straight red for a shocking tackle on Keatings.
Alloa head coach Grant said: “I thought my team were outstanding. Goals change games and the timing of the goals wasn’t ideal. I can’t give nothing but credit, their effort and commitment.
“It gave us a mountain to climb in the second half. We are second bottom of the league and our performances don’t deserve it. We need to be more ruthless in both boxes.”