Twice Dagenham lead. Matt Richie had the visitors in front as early as the 9th minute but Fryatt was on target just minutes later.
Ben Strevens put the visitors back in front on 25 mins but a Fryatt penalty on 30 mins had the scores level agian.
A tighter 2nd half saw Leicester edge in front when Fryatt scored his, and Leicester's third to eventually win the tie.
The Foxes go into tomorrow's 3rd round draw.