Miller, 20, who joined Albion on a season-long loan from Manchester City on Thursday, set the seal on the win with a stunning 71st minute strike.
Veteran marksman Kevin Phillips had fired Albion ahead with his second goal of the campaign seven minutes earlier as Tony Mowbray's side picked up their first points of the season.
But it was not the response that Preston boss Paul Simpson had wanted on the back of their Carling Cup defeat at the hands of Morecambe.
Failure to take advantage of their early pressure proved to be costly and they are still looking for their first goal of the season in the league after last weekend's stalemate with Norwich City.
Albion were fortunate to escape the opening exchanges unscathed as they struggled to keep Neil Mellor in check.
Mellor blocked a third minute clearance from Dean Kiely that dropped just wide of the post.
Mellor then saw his seventh minute drive well held by Kiely as Albion struggled to get a foot-hold in the game.
Brett Ormerod headed just wide after 18 minutes, before former Albion midfielder Darren Carter was denied a goalscoring return seven minutes later when Kiely dived bravely at his feet.
That escape finally saw Albion start to threaten themselves mainly through their Scotland international striker Craig Beattie.
Beattie headed straight at Wayne Henderson in the 28th minute before the former Celtic marksman flashed a shot wide nine minutes later.
Preston were then indebted to central defender Youl Mawene who deflected James Morrison's goalbound free-kick over the bar five minutes before half-time.
Albion carried their threat into the second half and, after Beattie had again seen his shot saved by Henderson, their pressure finally told.
Morrison ghosted down the left-wing and crossed for Phillips who had the simple task of heading into an empty net from three yards for his second goal of the season.
That effectively sealed Preston's fate and left the stage clear for Miller to steal the show.
He bustled his way clear from the halfway line and charged past Mawene before flashing his shot past the stranded Henderson.