Stephen Kenny's side temporarily move into second place after coming from behind in the Louth derby; for Mick Cooke's visitors, it's still only one win this season
Goals from Graham Rusk and Alan Brennan gave the visitors the lead before Keith Ward and John Dillon levelled the tie late on.
Drogheda took the lead after 19 minutes when Rusk deflected David Cassidy's effort into the net. Peter Cherrie stopped his side going further behind moments later, pulling off a great save to keep out Declan 'Fabio' O'Brien.
Dundalk were on the back foot for most of the game, and found themselves two goals down midway through the second half.
Ryan Brennan met Cassidy's cross after some good passing from the visitors.
However, in a dramatic two minute period, the game was level. Alan Byrne gave away a free-kick which Keith Ward converted, before the same player was sent off for a foul in the area. John Dillon took the penalty kick to give Dundalk a share of the spoils.
The draw sees Dundalk move up to second place in the table, but could find themselves seven points adrift after Sligo Rovers take on Bohemians on Friday evening.