Leading 2-0 from the home leg, the Israeli champions saw their advantage erased by two first-half strikes from Wanderson in Razgrad.
Ludogorets moved in front 11 minutes after the interval, with Marcelinho making it 3-0 on the night.
Hapoel needed to score to stay in the competition and an all-important strike from Mohammed Ghadir after 61 minutes kept the Israeli champions alive.
Resilient defending kept Ludogorets at bay and their frustrations boiled over in the last minute of added time when Wanderson was sent off.