Fir Park had not been a happy hunting ground for the Scottish champions in recent seasons but a double from Miller, an own goal from Steven Saunders and a Vladimir Weiss strike sealed the win, with John Sutton’s effort nothing more than a consolation for the Steelmen.
Motherwell had managed to beat the weather to ensure this clash went ahead amid further fixture chaos but failed to beat the visitors.
Boss Walter Smith paid tribute to Vladimir Weiss after his man-of-the-match performance.
“He played very well for us today and we are delighted about that. I thought he did very well.
“He’s a young man and when you are in a situation like that when you’re on loan from another club, it’s always awkward for a young player to handle the situation overall.
“He’s had a little bit of a struggle for consistency but that happens to all players of that type.
“He was excellent today and I’m delighted for him. He’s been on loan from his own club on a few occasions now and he is looking to get a bit of stability.”
A late goal in each half from Steven Thomson secured St Mirren maximum points at Inverness.
The Buddies came from behind to win at the Caledonian Stadium after Lee Cox netted from close range in the eighth minute.
Thomson’s 25-yard screamer levelled matters seconds before half-time and he hit the winner with five minutes remaining.
Craig Brown claimed victory in his first match in charge as Aberdeen moved off the foot of the Clydesdale Bank Premier League with a 2-1 victory at Easter Road.
After Derek Riordan scored his fifth goal in four games on the stroke of half-time to cancel out Yoann Folly’s first for the Dons, Scott Vernon bundled in a Paul Hartley cross which evaded a static Hibs defence after 62 minutes for the winner.
The result took Brown’s side three points clear of Hamilton at the bottom of the SPL and within two points of free-falling Hibs.