Mustoe pounced in the first minute of stoppage time to poke Terry Cooke's cross beyond Ben Roberts for his first goal for the club.
Teenager Chris Brunt had earlier given Wednesday the lead with his first senior goal but the strike of the game belonged to Richard Carpenter who scored with a 20-yard volley.
Former Chelsea chairman Ken Bates, this week, invited the current Wednesday board to publish the club's financial records. The 72-year-old believes Wednesday can be a Premiership force again but without the help of Turner, who he indicated would not be retained as manager should his takeover bid succeed.
To Turner's relief, his side took the lead through Brunt on eight minutes, the teenager curling a 25-yard free-kick over the wall and into Roberts' left-hand corner.
The 18-year-old Brunt, on-loan from Middlesbrough until the end of the season, was making his first start for the Owls. But his quality strike was eclipsed six minutes later by Carpenter's stunning volley from the edge of the area which looped over Kevin Pressman and into the top corner.
Brunt then engineered Wednesday's next attack on 18 minutes when his pinpoint cross found the climbing Cooke in front of goal but the winger headed over from six yards out.
Nathan Jones headed onto the top of Pressman's crossbar from 18 yards as half-time approached.
Second Division top scorer Leon Knight was kept quiet on his return to Hillsbrough after a troubled year with the Owls last term.