The result means third-placed Dortmund have failed to win at home in their last four games.
Bayer Leverkusen, second in the table, fared even worse as Freiburg twice rallied from a goal down to snatch a 3-2 victory with substitute Felix Klaus grabbing the winner in the last minute.
Leverkusen, who have now lost their last three league games, have 37 points from 18 games, 10 behind leaders Bayern Munich.
Dortmund are on 33 points, the same as fourth-placed Borussia Moenchengladbach who lost 2-0 to Bayern when the league resumed on Friday after a winter break.
"My team was far too tight, too cramped up," Dortmund coach Juergen Klopp said.
"We really wanted to set a marker today. I know we can play better."
Leverkusen went ahead after four minutes when Lars Bender's low 22-metre drive beat Oliver Baumann.
Admir Mehmedi's shot from the edge of the box drew Freiburg level before a header by Simon Rolfes put the visitors back in front after 35 minutes.
Jonathan Schmid again levelled for the home team before Klaus secured maximum points when he beat Leverkusen's offside trap.
Sven Bender was also on target, a minute after his twin brother Lars, as last season's Champions League runners-up Dortmund looked to end a run of three consecutive home defeats.
Bender then put the ball through his own net to draw ninth-placed Augsburg level.
Sahin floated a free kick over the wall and into the net in the 66th minute before the 22-year-old Ji, signed from English Premier League Sunderland earlier this month and then loaned out, broke Dortmund hearts with a diagonal header.
Ji also had a spell on loan at Augsburg last season.
Dortmund, who were already missing several starters through injury, lost Poland midfielder Jakub Blaszczykowski to a suspected torn cruciate knee ligament injury after six minutes.
Second from bottom Nuremberg finally recorded their first league win of the season, crushing Hoffenheim 4-0.
The victory prompted coach Gertjen Verbeek to shave off his beard after he vowed not to do it until they had won in the Bundesliga.
New coach Tayfun Korkut led Hanover 96 to a 3-1 triumph at VfL Wolfsburg, ruining the debut of former Chelsea midfielder Kevin De Bruyne.
Mainz 05 are eighth after substitute Benedikt Saller's 87th-minute goal clinched a 2-1 win at VfB Stuttgart.