Brendan Rodgers' men dropped into the competition after failing to make it out of the UEFA Champions League group stage, having only managed one victory in the campaign.
It looked as though Liverpool's underwhelming fortunes in Europe would continue at Anfield on Thursday, despite dominating possession for the most part.
Demba Ba was thwarted by Simon Mignolet having been sent clean through for Besiktas' best chance in the first half, before Alberto Moreno saw an effort tipped over by goalkeeper Cenk Gonen.
Chances were few and far between for both sides in the second half, despite the addition of Balotelli to Liverpool's frontline, but the Italy international was on hand to convert from the spot five minutes from time after Jordon Ibe had been felled by Ramon.
Steven Gerrard was sidelined with a hamstring injury, ruling him out of a reunion with Besiktas frontman Ba, who – then with Chelsea - pounced on a now-infamous slip by the Liverpool captain to contribute to the downfall of the Anfield club's Premier League title challenge last season.
An intruder on the pitch caused a momentary delay before the visitors' first chance fell the way of midfielder Veli Kavlak, but his shot was dragged wide of the left-hand post.
Kavlak came close once again shortly after the half-hour mark when he headed wide from a corner, and Mignolet had to get down well to keep out an effort from Ba after the Senegalese had been sent clean through on goal – the goalkeeper demonstrating what he should have done against Chelsea back in April.
Manager Rodgers brought on Balotelli to give his side a greater attacking presence with just over an hour on the clock and the Italian was almost instantly involved, curling a free-kick into the arms of Gonen.
Balotelli stepped up - after some discussion with stand-in skipper Henderson - to coolly slot into the bottom right-hand corner and send Liverpool to Turkey next week with a slim advantage.
