However, Zahavi did open the scoring with his next chance. The ball dropped to him after Stephan Schrock had failed to clear and the striker slotted in.
Frankfurt were unable to produce an immediate response to falling behind and it was Maccabi who had the next shot at goal, Barak Itzhaki firing over from 25 yards.
Itzhaki wasn't to be denied, however, as he headed in a left-wing cross to double Maccabi's advantage. The celebrations had barely finished when Itzhaki grabbed his second of the night with a chip over Trapp after Zahavi had been crowded out.
Frankfurt failed to produce much of note in the Maccabi half. Then Zahavi almost got in on goal but was denied by the away defence.
Srdjan Lakic brought the visitors back into the game with a header that found its way under the goalkeeper and into the net.
However, Frankfurt were unable to find an equaliser and Zahavi chipped in a fourth for the home side in stoppage time.