Promoted, injury hit Slazenger made a bright start but were playing catchup from the tenth minute.
A great strike from Julie Finch from a short corner was saved but Amy Smeaton touched the ball over the line to level.
But Dewsbury went into the break 2-1 up with a carbon copy of their opening goal.
Slazenger were indebted to their goalkeeper who kept them in with a shout until the third goal went in.
Lucy Ellis had a sound debut for Slazenger while Jackie Cooper got the team’s vote for player of the match.