Former Glover Gavin Williams tapped in the only goal of the game from close range in the 76th minute after a dazzling dribble by skipper Will Hoskins.
Oli Johnson, Dean Bowditch and Andrew Welsh had all previously gone close for the hosts.
"We rode our luck and we are delighted to have come away with a 1-0 win. To win any match we need a bit of luck and we had more than we would normally get," said Campbell. "The lads defended for their lives winning headers and there were great saves by Conrad Logan. It was tremendous.
"Over the past five games (since he took over as manager) we have given 100% and if you have a following like we had here it is priceless."
On the winning goal from Williams, Campbell added: "We know Yeovil means a lot to Gavin and when he scored he didn't celebrate. But when he came on as substitute he was excellent."
Source: PA
Source: PA