Roberts came to the Daggers' rescue on several occasions before they took the lead against the run of play after 30 minutes when leading scorer Romain Vincelot was completely unmarked to head in Darren Currie's corner.
Just three minutes later the Glovers were level though when Ollie Johnson did beat Roberts but Jon Nurse's 72nd-minute strike have Dagenham the win.
"We're delighted, it's a fantastic three points for us. It certainly didn't look that way come half time and we were very fortunate to be in the game," said Burnett.
"We went in at 1-1, changed a few things and come out and put in a much better performance in the second half.
"Tony Roberts pulled out three very good saves. One of them was top drawer. He's a very good goalkeeper and 'Robbo' has made many saves this season to keep us in games. We were very fortunate to go in even at half time, but we've come out in the second half and played better."
Source: PA
Source: PA