Having also drawn 1-1 at Hoffenheim on Wednesday, Dortmund fell further behind champions Bayern ahead of next Sunday's top-of-the-table clash against the Bavarians at Munich's Allianz Arena.
Bayern are the only team in Germany's top flight to have won all seven league games so far.
Pep Guardiola's leaders are looking to become the first team to win four consecutive Bundesliga titles.
After Marcel Heller gave Darmstadt a shock lead, Gabon striker Pierre-Emerick Aubameyang looked to have sealed the hosts' comeback win with two second-half goals to maintain his record run having scored in each of Dortmund's first seven Bundesliga games.
With nine goals, Aubameyang is just one behind Bayern striker Robert Lewandowski.
But Darmstadt captain Aytac Sulu rescued a point by stabbing home from a free-kick just before the final whistle as the Dortmund defence failed to react in time.
"Our problems came from the final free-kick, there were four or five players just standing around and that was no way to defend against a simple set-piece like that," fumed Dortmund captain Mats Hummels.
Earlier, midfielder Vladimir Darida rescued a point for Hertha Berlin with the late equaliser in their 1-1 draw at Eintracht Frankfurt after captain Alexander Meier gave the hosts the lead midway through the first half.
The point leaves Hertha sixth and Frankfurt 10th in the table.
On Saturday, Bayern took the chance to extend their lead with a 3-0 win at Mainz as Lewandowski's goal haul continued.
Having sent German league records tumbling last Tuesday with five goals in just nine minutes after coming off the bench in the 5-1 rout of Wolfsburg, the 27-year-old claimed two more against Mainz.
Lewandowski scored his 100th Bundesliga goal by heading Kingsley Coman's cross inside the far post on 51 minutes and pulled up his jersey to reveal a T-Shirt which stated: "100".
"The T-Shirt was my idea, I didn't know if I'd score today, but you always have to think positively, which is why I had it made," he told reporters.
An Arturo Vidal pass then put Lewandowski in behind the defence to round the goalkeeper for his 101st on 63 minutes.
France Under-21 winger Coman grabbed Bayern's third five minutes later with a simple tap in from a Douglas Costa cross.
Bayern's next date is hosting Dinamo Zagreb in the Champions League on Tuesday.
Schalke remain third after Germany Under-21 attacking midfielder Leroy Sane scored for the third game in succession to seal Saturday's 1-0 win at Hamburg with a superb strike on the hour.
Bayer Leverkusen, who play European champions Barcelona away on Tuesday, romped to a 3-0 win at Werder Bremen with goals by Swiss forward Admir Mehmedi, winger Kevin Kampl and Germany Under-21 talent Julian Brandt.
Wolfsburg, who play Manchester United at Old Trafford on Wednesday in the Champions League, dropped more points in a 1-1 draw at home to bottom side Hanover to stay fourth.
Bas Dost's header was cancelled out by Japan midfielder Hiroshi Kiyotake's superb volley on 57 minutes.
Borussia Mönchengladbach, who host Manchester City on Wednesday, picked up their second win since Lucien Favre's shock resignation last Sunday with a 3-1 victory at VfB Stuttgart.
The goals came from Granit Xhaka, a Christian Gentner own-goal and Raffel's late effort afer Daniel Ginczek slotted a 40th-minute penalty for Stuttgart.
Hoffenheim climbed to 15th with a 3-1 win at Augsburg as Germany international Kevin Volland scored twice, including a second-half penalty.