The left-back smashed one in from the edge of the area before converting a penalty – his 10th success from the spot to maintain his 100pc Premier League record.
Substitute Shane Long pulled a goal back midway through the second half but the Baggies, who had won just once in their previous 13 league visits here, saw their recent slump extended to just one point from a possible 15.
Fans would also have been questioning manager David Moyes before kick-off after he dropped Nikica Jelavic.
Even accounting for his lack of recent form the striker, substitute in a Premier League match for the first time since March 13, looked a bold one.
However, Moyes probably reasoned the Croatia international, who had not scored against top-flight opposition in seven matches with his last strike being the last-minute winner against Tottenham on December 9, needed either a break or a wake-up call.
But it was a surprise that in his absence Baines was the player to step up to the mark in front of goal, even if one was from the spot.
Despite some late Baggies pressure, Everton closed the gap on fourth-placed Tottenham to a point.