The visitors made most of the early running but struggled to find the killer touch before Webster broke the deadlock on 34 minutes.
A Jambos corner was cleared only as far as the defender and he drilled the ball back through a crowded box and into the net.
Andrew Driver and David Templeton had chances to extend the lead after the interval but they had to wait until after the hour before they could settle the match.
Templeton was felled on his way into the area and Sutton stepped up to calmly convert the resulting spot-kick.
Alex Whittle and Ryan Wallace had late chances to claw one back for the hosts but Jamie McDonald was equal to both to earn his clean sheet.