Dortmund, who had won 14 of their 16 previous games and lost just one, needed only a point in their final game before the winter break to equal Bayern Munich's record of 44 points from 17 games in the 2005/06 season but with a better goal difference.
They were denied it when Gekas completed a swift attack with a classy left-foot finish in the 87th minute - a 14th goal of the season for the Bundesliga's top scorer.
Dortmund's first defeat on the road this season - after winning a record eight out of eight away games - left them top with 43 points from 17 matches.
Seconds before the Gekas goal, Dortmund striker Lucas Barrios had fired high over the bar from close range to squander the visitors' best chance.
"There was no team that deserved to win it," Dortmund coach Jurgen Klopp said. "We missed the huge chance a minute earlier with Lucas and if he had scored we would have won it. But we should not lose our optimism. Luck was just not our side today."
Werder Bremen's disappointing season continued with a 2-1 defeat against visitors Kaiserslautern with both teams finishing with 10 players.
