Expert penalty-taker Daems converted from the spot for his third goal of the season in the 76th minute to lift Gladbach, who had to come through a relegation play-off last season to stay up, to 16 points.
Last season's champions Dortmund needed a 90th-minute goal from Lukasz Piszczek to beat battling Mainz and snap their two-game losing streak to move up to eighth.
Piszczek, whose poor back-pass was to blame for Mainz's 33rd minute lead through Nicolai Muller, made amends and rifled in from outside the box, seconds before the final whistle.
Dortmund, who had playmaker Mario Gotze back from suspension and welcomed back striker Lucas Barrios from injury for the first time this season, had levelled in the 64th minute with Ivan Perisic's first Bundesliga goal, a clever low drive.
Schalke 04 came good on their promise to put in a stellar performance against Freiburg for coach Ralf Rangnick who surprisingly stepped down on Thursday citing exhaustion, winning 4-2.
VfL Wolfsburg, playing with 10 men for the entire second half following the dismissal of defender Sotiris Kyrgiakos, beat Kaiserslautern 1-0 with Ashkan Dejagah's diving header on the hour securing the points for Felix Magath's team.
