At the Benteler Arena, Bayer Leverkusen were looking for three points on their travels that would see them move into the UEFA Champions League places.
Strugglers Paderborn thwarted their more illustrious opponents for almost three quarters of the match, but the hosts' resistance was finally broken when Kyriakos Papadopoulos headed home Gonzalo Castro's free-kick in the 73rd minute.
Roger Schmidt's men wrapped up the points with six minutes left on the clock when Son Heung-min tapped home from close range, before the South Korea international bagged his second late on in a harsh blow to Paderborn.
Earlier in the day Cologne moved up to 11th thanks to their win over Frankfurt in front of a 50,000 sell out at the Rhein Energie Stadion.
The hosts were leading 3-1 by the time Ujah drilled home their fourth goal in the 82nd minute.
Ujah celebrated by running to the touchline to grab hold of Hennes, a goat named in honour of former player and coach Hennes Weisweiler, before grabbing the animal's horns.
Alexander Meier reduced the deficit with his second from the penalty spot in stoppage time, but it was not enough to prevent Frankfurt's European hopes taking a blow.
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