Second-half strikes from Graeme Holmes and Edward Ferns gave Alloa their first victory of the Championship season.
Willie Gibson and Grant Gallagher missed early chances for the hosts before Alloa's Michael Chopra and Holmes failed to hit the target.
The Wasps took the lead as Dumbarton reacted slowly to a quickly-taken free-kick; Holmes finishing past Mark Brown.
Robbie Crawford and Grant Gallagher came close, but Ferns sealed the win in stoppage time.
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