Miller, 20, and Phillips, 34, helped themselves to a goal in each half to send Norwich crashing to a sixth successive away defeat.
On-loan Manchester City striker Miller took his goal tally for the season to eight - with six coming in the last seven games - while Phillips also has eight goals to his name from just nine games.
Luckless Norwich were never really in contention, apart from a brief flurry at the start of the second half.
But for three goal-line clearances and goalkeeper David Marshall they would have crashed to an even heavier defeat.
While City were full of effort, and the odd piece of skill from Darren Huckerby, they lacked the cutting edge that Albion possessed in Miller and Phillips and that was the key difference between the sides.
Albion laid siege to the Norwich goal straight from the kick-off and it was a surprise they had to wait as long as 16 minutes to break the deadlock.
Jonathan Greening and Miller both had shots blocked as early as the second minute before Phillips saw his drive tipped over the bar by Marshall.
Martin Albrechtsen then headed wide from a Greening corner before Norwich's luck ran out.
Another Greening corner caused chaos in the Norwich area, and when Bostjan Cesar nodded the ball back across the face of goal, Miller was on hand to head home from six yards.
Albion should really have added to their lead before half-time but Paul Robinson and Phillips had efforts cleared off the line by Darel Russell and Simon Lappin respectively - both from Greening corners.
Norwich enjoyed their best spell of the game at the start of the second half when a Jamie Cureton cross was deflected over his own bar by Albion central defender Albrechtsen.
Huckerby then shot narrowly wide but it proved to be a false dawn as Albion sealed their success through Phillips in the 51st minute.
Miller raced clear down the left wing and crossed for Phillips to nod home at the far post.
Sixty seconds later, Miller was denied a second when his header was cleared off the line by Lappin.
Marshall then denied Phillips his second with a smart save in the 73rd minute when the former England striker only had the City goalkeeper to beat.