Romain Vincelot put the Daggers ahead in the 76th minute but the Grecians hit back in style.
Matthew Taylor headed an 81st-minute equaliser and Richard Logan then buried a fine cross from Daniel Nardiello to settle matters.
Tillson said: "We are very pleased with the result. I thought we were very competitive right from the start.
"These are very difficult games and we are trying to get as many results and performances between now and the end of the season.
"We knew what we were going to get. They are a very tough team and were very competitive, which gave us a great chance to get into the game and play some good football."
Source: PA
Source: PA