Jens Langeneke put the away team in front from the penalty spot in the 11th minute, but goals from Nils Petersen and Kevin de Bruyne earned Bremen all three points at the Weser Stadion to take them up to seventh in the Bundesliga.
Fortuna's seventh successive game without a win leaves them on the brink of the bottom three with Wolfsburg able to go above them with at least a point from their game against Hoffenheim on Sunday.
Schaaf was alone on the Bremen bench for the first time in 13 years after his right-hand man Klaus Allofs left for Wolfsburg during last week, and a new era for the northern Germany side could hardly have got off to a worse start as Sokratis Papastathopoulos gave away a penalty after just 10 minutes.
He chose an irregular way to end Robbie Kruse's dash for goal and Langeneke stepped up to the spot, keeping his cool to put the visitors in front.
Papastathopoulos lost Kruse again in the 23rd minute and he set up Ken Ilso, who wasted a great opportunity to double Fortuna's lead with only Sebastian Mielitz to beat.
Schaaf was furious on the sidelines, making his anger clear to his own team, who struggled to respond.
His words probably got even louder in the dressing room at half-time as Bremen emerged with a much more positive approach to the second 45 minutes.
Petersen brought them level just five minutes in, heading in Lukas Schmitz's cross just a minute after failing to reach a similar ball from the left.
The left flank was becoming increasingly productive for Bremen, who were now gaining control of the proceedings and threatening a second goal.
Petersen and Eljero Elia both wasted good chances before the hosts were reduced to 10 men when Lukimya, who joined Bremen from Fortuna in the summer, earned a second yellow card for a foul on Kruse.
Bremen continued to push for a winner, even with 10 men, and they found it in the 82nd minute when De Bruyne scored his fourth goal of the season.
Aaron Hunt's cross was deflected out to the on-loan Chelsea midfielder, who demonstrated his eye for goal with an instinctive finish to earn Bremen the points.