Carlo Monti's penalty was enough to earn Dundee a 1-0 victory at Alloa.
The Wasps almost took the lead early on, but Andrew Kirk's header was cleared off the line at the back post.
Ryan Conroy had the best chance of the first half for Dundee but fired his shot across goal and wide.
James McCallister's effort early in the second half was well saved by Scott Bain.
Dundee's pressure told on the hour mark when Monti was hauled down in the box by Daryll Meggatt. He picked himself up and unleashed an unstoppable penalty into the top corner.
Peter MacDonald almost doubled the lead in the final minute but his header hit the bar and bounced over.