The match in Besiktas's Vodafone Arena saw the Black Eagles control the game from the very start, earning a comfortable 2-1 victory over the Israeli visitors.
Besiktas, who won the first leg 3-1 last Thursday, scored on the 17th minute when Cameroonian forward Vincent Aboubakar's superb strike found the net.
Thanks to Aboubakar's first ever Europa League goal, Besiktas managed to control the pace and did not let Hapoel Beer Sheva threaten the home side’s goal.
However, despite leading the first half 1-0, Besiktas could not hold on and the visitors equalized on the 64th minute when Anthony Nwakaeme completed a left-wing cross with a low left-footed shot.
Brought on in the 79th minute, in-form striker Cenk Tosun made the score 2-1 near the end of normal time minute with a shot delivered after driving into the edge of penalty area.
With the win, Besiktas moved into the last 16 and are the only Turkish team left in European club competitions.
Below are the rest of the Round 32 results so far:
Fenerbahce - Krasnodar: 1-1 (Krasnodar advanced on a 1-2 aggregate score)
Schalke 04 - PAOK: 1-1 (Schalke advanced on a 4-1 aggregate score)
St. Etienne - Manchester United: 0-1 (Manchester United advanced on a 4-0 aggregate score)
Osmanlispor - Olympiacos: 0-3 (Olympiacos advanced on a 0-3 aggregate score)
Ajax - Legia Warszawa: 1-0 (Ajax advanced on a 1-0 aggregate score)
APOEL Nicosia - Athletic Bilbao: 2-0 (APOEL Nicosia advanced on a 4-3 aggregate score)
Zenit St. Petersburg - Anderlecht: 3-1 (Anderlecht advanced on a 3-3 aggregate score decided on away goals)
Roma - Villarreal: 0-1 (Roma advanced on a 4-1 aggregate score)