The home side made a flying start in the fifth minute when a well-worked set-piece routine found Evans at the back post and the defender headed home.
Chris Hughton's side rarely posed a threat in the first half and the closest they came to threatening Ben Foster's goal was when Jose Izquierdo curled a shot over the bar.
The Baggies doubled their advantage 10 minutes after the break when Chris Brunt swung in a corner and Dawson rose highest to head past Matt Ryan.
Brighton never really threatened to get themselves back into the game and Anthony Knockaert trying a shot from distance was all they could really muster.
Pardew's side held out for the win, which was his first in charge and his team's first in 20 matches as they look to move themselves out of the relegation zone.