Werder stumbled in the previous round, suffering an unpleasant defeat to Heidenheim, but they quickly bounced back with a 1-0 victory over Cologne.
Both teams had a good chance in the first half, but the outcome was settled in the second half.
Niemann entered the field in the 66th minute and found the net just four minutes later. Weydandt crossed from the right side, the goalkeeper misjudged the ball, allowing the German to pounce on it and slot it into the empty net.
Werder managed to maintain their lead until the end of the match, keeping their hopes alive for a European spot as they chase Eintracht Frankfurt, who are three points ahead with a game in hand.