Leading scorer Gavin Tomlin bagged a fine double and midfielder Kevan Hurst also netted as the visitors stretched their impressive unbeaten run to 14 matches in all competitions.
"Sometimes when you score as early as we did it can be worrying because complacency can seep in, but to be fair the players were very professional in their approach," said Sturrock.
"We went about our business from the first minute to the 93rd. It was a great win.
"It's the kiss of death going this long unbeaten, so we've got to keep churning out results.
"I'm delighted. Our final pass let us down a wee bit, but you can't knock three goals away from home.
"We didn't really kill them off in the second half and you've got to give credit to Dagenham for going right to the end.
"The player are level-headed and are just taking each game as it comes. They're all in this together."
Sturrock's side needed just 54 seconds to take the lead and it was former Dagenham striker Tomlin who struck from close range against his old club.
Tomlin bagged his second, and 14th goal of the season, to double the visitors' lead after 14 minutes and Hurst put the contest out of reach when he found the top left corner with a superb strike 10 minutes after the break.