In-form Miller capitalised on Kerry Mayo's defensive hesitancy to head the ball past goalkeeper Michel Kuipers after 21 minutes.
For Brighton, Dean Hammond saw his strike hacked off the goalline by Joleon Lescott, and Darren Currie's free-kick dipped just over the bar.
Wolves manager Dave Jones:
"It was not the best performance because we should have killed Brighton off.
"The longer the game went on the more edgy we became and by the death we were looking nervous.
"It was our first win and it was a particularly hard three points. Brighton is a difficult place to come and play and they made it hard for us."
Brighton: Kuipers, El-Abd (McPhee 56), Cullip, Butters (Harding 65), Mayo, Currie, Hinshelwood, Hammond, Nicolas (Jarrett 85), Virgo, Knight.
Subs Not Used: Oatway, May.
Wolverhampton: Jones, Clyde, Naylor, Lescott, Craddock, Newton, Ince, Seol (Cooper 78), Olofinjana, Miller, Cort.
Subs Not Used: Oakes, Cameron, Andrews, Clarke.
Goals: Miller 22.
Ref: T Leake (Lancashire).