Saints had taken a shock lead at Ibrox on Saturday through Danny Grainger, before Sasa Papac – who netted both his goals against the Perth side last term – restored parity with a little help from unfortunate defender Kevin Rutkiewicz.
But it was Miller who had the final say as he claimed his fifth goal of the season to add to strikes against Kilmarnock and Hibernian in Rangers’ previous SPL outings.
Nikica Jelavic was named on the Rangers bench after being granted a work permit, while fellow new recruit Vladimir Weiss made his first start for the champions.
Lee McCulloch made his first appearance of the SPL season after returning from suspension but Kyle Lafferty was suspended.
Saints brought in Steven Anderson, Jody Morris and Marcus Haber, changing their line-up following the win over Morton in the League Cup in midweek.
The hosts had the chance to put their visitors under pressure early on with a free-kick from 25 yards that was struck well enough by Papac but comfortably smothered by goalkeeper Graeme Smith.
At the other end, Morris saw his shot from distance take a deflection off team-mate Collin Samuel and fall wide, before Allan McGregor was called into action to block from Haber at his near post.
Weiss and Steven Davis linked up well with a one-two before the on-loan Manchester City winger had a crack at goal, but the end product was weak and, again, Smith was untroubled in the Saints goal.
The Perth side were forced to make a change with 20 minutes gone when Murray Davidson left the pitch on a stretcher following a clash of heads with Haber and was replaced by Liam Caddis.
The visitors nevertheless went ahead after 25 minutes when a corner from Morris was collected by Danny Grainger 20 yards out and he lashed past the outstretched hands of McGregor and high into the back of the net.
However, Saints’ hopes of holding their lead at least until half-time were dashed when the home side hauled themselves back onto level terms after 33 minutes.
A lovely cross from Weiss found Steven Naismith at the back post and his header was collected by Papac, who tried to force over the line from a yard out, with Rutkiewicz’s attempt to clear only helping the ball into the net.
Rangers piled forward in numbers but could not claim the advantage before the interval despite their pressure in front of goal.
Home fans appealed for handball against Alan Maybury a few minutes after the restart but those pleas for a penalty were ignored by referee Callum Murray.
Rangers continued to push for another goal and Weiss weaved his way into the box from the left before cutting back for McCulloch, who saw his shot fizz narrowly past the post.
There was a second claim for a Maybury handball but, again, the match official refused to point to the spot.
Rangers had another decent chance when Madjid Bougherra made one of his surging runs down the right flank before whipping a dangerous cross into the box, but Smith was able to punch to safety as James Beattie loitered with intent.
The former Stoke striker then made way for Jelavic, whose introduction for his debut after 67 minutes was met with noisy approval from the crowd.
The referee had another call to make when Weiss went to ground in the box under pressure from Grainger but the youngster succeeded only in earning himself a yellow card for dissent when his claims were dismissed.
Rangers’ hard work eventually paid off when Miller claimed his fifth goal of the season with 11 minutes to go.
Papac began the move with a short ball to McCulloch who swept it into the path of Miller and he shrugged off Maybury before rifling home from the edge of the box.