The Bundesliga side lost midfielders Nicolas Hofler and Karim Guede to red cards at the end of a match devoid of entertainment and inspiration.
The hosts had the better of the chances without seriously testing Freiburg goalkeeper Oliver Baumann.
The draw kept both sides in the bottom two spots in Group H, with third-placed Freiburg three points behind Slovan Liberec in second. Estoril are four points off the Czech side.
Luis Leal was just about the most lively player on the pitch on Thursday night and he worked Baumann in the 14th minute, forcing the German into a save with his feet with a shot from the left side of the area.
At the other end Oliver Sorg fired wide and Vladimir Darida's long-range free-kick was held by Vagner.
Leal had another sight of goal just before the half-hour mark, but dragged his right-footed shot wide of the far post.
The match threatened to burst into life early in the second half when first Baumann did well to punch away a powerful Seba header from a Leal cross and then his opposite number Vagner parried a Darida shot.
But the moments of excitement continued to be rare.
Baumann had to be alert to push away Carlitos' header from a Yohan Tavares corner and was called into action once more when he punched clear Evandro Goebel's free-kick.
A game desperately lacking in quality scarcely deserved a winner, though, and instead finished with two late red cards.
Hofler picked up a second booking in the 87th minute and Guede repeated the trick two minutes later to leave Freiburg with nine men, but they held on to a point.