Sheridan struck in the fourth minute, following up Connall Murtagh's header from a corner to fire the Welsh side to a Europa League qualifying round first-leg victory in Rhyl.
The visitors provided a stern test over the game and pushed hard for a equaliser to take back to Estonia, but home keeper Ashley Morris pulled off a number of impressive saves.
Ilja Antonov also fired just over the bar from outside the area and Artom Artjunin struck a free-kick against the post.
It could have been even better for Bala but former Wrexham midfielder Mark Jones' shot from the edge of the area was pushed on to the post by Roman Smishko.
The result is even more impressive for the fact that Bala only returned to training two weeks ago, while Levadia are midway through their domestic season.
Bala will take their one-goal advantage to Tallinn for the second leg on Thursday, 11 July.