Iain Hume prodded home Martin Woods' cross from the left after 24 minutes when Pompey goalkeeper Mikkel Andersen and skipper Brian Howard hesitated to clear.
Saunders' men have won six of their nine games on the road, compared to three out of eight at home. The Welshman was delighted with a rock-solid display from his side and hopes it can help them boost their home record.
"I'd like us to win some games for our supporters who come and watch us every week. I'd like them to see us winning a bit more and it will come," said Saunders. "But it was another great win for us. We showed a lot of determination and the back four defended great. I don't know if the goalkeeper had a save to make really.
"We should have killed them off really. We had loads of chances. Halfway through the second half, they had loads of balls going into their box and we didn't go to 2-0 up.
"Some of the football we played at times was excellent. We made some mistakes and we can still get better but it was another great win."