Albion had not come from behind to win since the 3-2 home victory over Swansea City last November - but they had to this time after being stung by a rapid Burnley break.
Having won possession upfield when summer signing Horn Myhre went down meekly under a challenge from Hannibal Mejbri, Burnley transferred the ball upfield.
Jacob Bruun Larsen drifted left to drill over a wicked left-footed cross and the helpless Styles was airborne as he arrived to meet it in an attempt to clear the danger on the edge of the six-yard box, only to clumsily turn it into his own net off his back heel - a similar mishap to Bristol City's lategoal just a few miles away at Birmingham the previous evening.
Albion deservedly levelled 10 minutes later when Burnley failed to recover after Price's cross from the left was deflected. Jimmy-Jay Morgan challenged, and Whitwell found the bottom corner with a low left-foot shot that nutmegged a visiting defender on its way in.
Three minutes after half-time, Price turned from creator to scorer when he took a superb first touch before curling in a right-footed beauty from 20 yards. And he was back on the scoresheet on 65 minutes when Albion won a soft penalty.
Whitwell made a run into the area and made contact with Burnley's Bashir Humphreys, and referee Anthony Backhouse pointed to the spot, enabling the confident Price to send Burnley keeper Max Weiss the wrong way.