Ross Stewart's goal separates the sides, meaning the tie remains on a knife-edge ahead of the return leg at Hillsborough, where the Owls have an outstanding record this season.
Boss Alex Neil was left a touch frustrated that their sides could not make more of some excellent chances at the start of the second half, but had no qualms with his side's overall display.
And he spoke of his delight at managing in front of a crowd of almost 45,000, the largest attendance in EFL play-off history.
The return leg takes place on Monday night but will Neil make any changes? Here, we take a look: