David McMillan drilled home low into the corner from 10 yards out in the third minute to give Dundalk the lead.
The hosts were reduced to 10 men in the 55th minute when Chris Shields was sent-off for a second yellow card.
Barry McNamee hammered in the equaliser on 67 minutes after Rory Patterson's low effort cannoned off the post.
Harry Monaghan had made the original break and picked out striker Patterson.
The league champions had a good chance to clinch all three points three minutes from the end but Stephen O'Donnell's brilliant header was superbly saved by Ger Doherty.
The Candystripes remain unbeaten in five league fixtures, having won their previous four matches prior to this game.
Kenny Shiels's side will entertain Shamrock Rovers at the Brandywell in their next league outing on Friday 8 April.
Derry City remain level on points with leaders Dundalk at the top of the Premier Division after drawing 1-1 with the champions at Oriel Park on Friday.