Early on Peter Canero's right-wing free-kick precipitated havoc in the box where David Connolly teed the ball up for James Scowcroft to finish.
With Wolves reeling, Leicester almost added a second as a Lilian Nalis shot rattled the crossbar.
Wolves, still without a Championship win this season, pulled level when Miller latched onto Paul Jones' clearance, and rifled past Ian Walker.
Leicester manager Micky Adams:
"I had 11 players out there who, if not having completely answered their critics, at least showed enough to suggest we're on our way.
"People have been saying things about our football club this week that we haven't been too happy about but if people leave us alone we'll be okay.
"We're not happy about what's been said but the only way to answer those people is on the pitch.
"The players, the backroom staff and the people in the board room are all working hard, getting their heads down and getting on with their jobs."
Wolverhampton: Jones, Clyde, Lescott, Craddock, Naylor, Newton,
Ince, Cameron (Cooper 78), Olofinjana, Miller, Clarke.
Subs Not Used: Oakes, Andrews, Sturridge, Lowe.
Booked: Ince, Clarke.
Goals: Miller 52.
Leicester: Walker, Canero, Keown, Heath, Tiatto (Gillespie 83),
Scowcroft, Nalis, Gemmill (Gudjonsson 71), Stewart, Dublin,
Connolly (Blake 76).
Subs Not Used: Benjamin, Dabizas.
Booked: Tiatto, Gudjonsson.
Goals: Scowcroft 4.
Ref: A Bates (Staffordshire).