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Steve Torpey capitalised on the first sending off by putting the ball in the back of the net from a free-kick, while Peter Beagrie punished the second offence by beautifully converting the resulting penalty.
Manager Brian Laws said: "It is a very good point to be honest. I think we played very poorly today, we have played a lot better.
"We struggled in the first half when we didn't pass the ball well enough. We started much better in the second half and it was against the run of play that Darlington went 2-0 up.
"At that stage we looked down and out but their indiscipline has cost them dearly with two red cards and has let us back in the game."
Darlo players Ryan Valentine and Barry Conlon were both shown straight reds for altercations with teenage Iron defender Andy Butler.
The final whistle saw Butler confronted by the home players and attracted vocal criticism from the home fans - but Laws poured scorn on suggestions that there was no contact.
He added: "You cannot go round headbutting players. They might claim there was no contact but Andy Butler has finished the game with a suspected broken nose and a badly cut lip.
"He is an honest young lad and doesn't go down for nothing."