Aaron Downes was the hero for Torquay as he pounced to net the only goal just after half-time, making it back-to-back wins for the visitors.
They began the day at the bottom of the table but are now in front of Knill's old club Bury as well as Northampton.
Knill said: "I can't praise the players highly enough. They've worked so hard all season, really, but these last two games have seen them gain the reward they deserve.
"We've had our difficulties this season, but here the players showed bags of character to keep a good side like Dagenham at bay.
"We knew it would be a tough test for us here but the lads have stood up to everything they threw at us and we've come away with a really important three points.
"We're only looking up now. That has to be the attitude to take into the busy Christmas period.
"It's a always a difficult time of the season with games coming thick and fast, but this gets us off to a pleasing start and there's plenty of confidence in the camp.
"From front to back we've put in a great effort and I'm delighted for the travelling fans too.
"For them to come all this way the weekend before Christmas is something the lads and I are grateful for. Their support has been great."