The visitors' confident start was rewarded with an eighth minute lead when Mark Arber found Sam Saunders, whose low cross was turned in at close range by Matt Ritchie.
But their joy was shortlived with City levelling within a minute when Fryatt took a return pass from Nicky Adams before ramming the ball home from eight yards.
Tony Roberts was then at full-stretch to keep out Fryatt's well-struck free-kick from 20 yards.
Undeterred, the Londoners continued to press and from a quick break edged themselves back in front on 25 minutes after David Martin had beaten away Ritchie's shot and Ben Strevens was there to sweep home the loose ball.
But they were soon pegged back again when on 28 minutes Magnus Okuonghae handled inside the box with Fryatt stepping up to score from the penalty spot.
The chances continued to flow with both keepers in the thick of the action.
First Roberts spread himself to keep out a close-range header from Aleksandar Tunchev and then Martin had to dive smartly to his left to get a hand to Ritchie's low drive.
City found themselves in front for the first time on 55 minutes when Marc Edworthy picked out Fryatt, who completed his hat-trick with a superb right-foot chip over the advancing Roberts.
The second half was a much tighter affair with Dagenham having to wait until the 71st minute for their next worthwhile attempt when a fierce Saunders free-kick forced Martin to palm the ball away for a corner.
And then when Martin was beaten by a header from Peter Gain, substitute Mark Davies was there for City to clear the ball off the line.