Onismor Bhasera gave the Pilgrims the half-time lead but James Beattie equalised after 57 minutes.
Stanley goalkeeper Paul Rachubka then turned from hero to villain in the 1-1 draw.
Rachubka, on loan from Leeds, kept out Warren Feeney's penalty with just 12 minutes left after Michael Liddle was adjudged to have brought down substitute Paris Cowan-Hall.
But he was then sent off in injury time after reacting when Feeney followed up a loose ball and challenged him.
Fletcher said: "We haven't played great but we have dug in and so we are delighted with a point.
"We did not do some of the basics right but to have an off-day and get a point away from home on a wet, windy, slidey pitch makes it a good point for us.
"Quality-wise it was a little bit few and far between and Feens [Feeney] has taken the last two penalties and this one didn't go in but that's the way it goes sometimes.
"Reg [Rene Gilmartin] has made some great saves but that's what he is there to do. There are positives to be taken from this game and build on."
- Sports & Recreation
- Warren Feeney
- Onismor Bhasera
- Paul Rachubka
- James Beattie
- Michael Liddle