The Light Blues passed up a series of chances with Hoops goalkeeper Fraser Forster making key saves to keep the game scoreless at the interval.
Click Here: liverpool mens jersey
Rangers were punished for those missed opportunities when Celtic defender Christopher Jullien knocked in a Ryan Christie free-kick in the 59th minute.
Forster then saved a penalty from Alfredo Morelos, after Hoops right-back Jeremie Frimpong had been sent off by referee Willie Collum for fouling the striker inside the box.
Neil Lennon’s 10 men held out for their 10th consecutive trophy win and his first success in the tournament as a manager, as Celtic delivered a psychological blow to Rangers, who have gone eight years without a major piece of silverware
This was another epic final between the two Glasgow giants.