A crowd of 1,682 saw Trinity, who lost their opening fixture last Saturday, take an 11th minute lead when Ashley Worsfold shot the ball through keeper Adam Bartlett`s legs after a fine through ball by Craig King.
The Quakers were back on level terms within 12 minutes though when Mark Beck headed in a Gary Brown cross.
And the hosts would go into the break in front when, following a Josh Gillies corner, Terry Galbraith (pictured) helped the ball on for David Syers to make it 2-1 after 42 minutes.
It got even better for Martin Gray`s men 4 minutes after the restart with a rather fortuitous goal to make it 3-1 – Galbraith`s cross going straight in over Trinity keeper Richard Walton.
Credit the visitors though, who fought back within 2 minutes, Ioan Evans heading past Bartlett at the near post.
That gave Dave Frecklington`s side momentum and on 64 minutes they deservedly pulled themselves back on level terms when Nathan Jarman headed home a Tom Davie cross.
However, with 17 minutes remaining, Darlington made it 4-3 when good work from Syers ended with Gillies firing home from just inside the box.
The Quakers held firm after that to make it a 100% start, while Trinity will be concerned after conceding 6 goals in their opening two matches.