Goalkeeper Adrian kept out Tammy Abraham’s spot kick to secure victory for the Champions League winners.
Chelsea had taken the lead in the first half through Olivier Giroud’s clinical strike but Sadio Mane scored twice to give Liverpool the lead.
Jorginho’s spot-kick took the game to penalties, where Liverpool triumphed.
The win comes just two months after Jurgen Klopp won his first trophy as Liverpool boss when he led the Reds to a 2-0 win over Tottenham in the Champions League final.
Games between these two sides in Europe have historically been tight affairs, with just one of their 10 previous meetings having been won by a margin of more than one goal.
It was the same again on Wednesday night as the two teams tussled for 120 minutes in a game that did not finish until almost 1am in Istanbul.
In the end, it came down to who could keep their cool in the sweltering heat and after nine excellent penalties, Abraham placed his shot too close to Adrian to hand Liverpool their first silverware of the season.
Fairytale final for Adrian
Two weeks ago Adrian was without a club, having been released by West Ham at the end of last season.
But, following Simon Mignolet’s departure to Club Brugge, Klopp snapped up the 32-year-old shot-stopper to provide experienced cover for Alisson.
Adrian had barely had time to get to know his new team-mates when he was called upon earlier than expected as Liverpool’s first-choice goalkeeper injured his calf in the 4-1 win against Norwich in the Premier League’s season-opener last Friday.
With Alisson facing a spell on the sidelines, Adrian made his full debut against Chelsea. It was his first competitive start since January, but he showed little signs of nerves or rustiness, catching the eye in the first half when he sprung off his line to deny Mateo Kovacic from close range.
There was little he could do about Chelsea’s opener, which was a clinical finish by Giroud, although he did give away the penalty deep in extra time when he took the legs of Abraham.
But that gave him the platform to produce his penalty shootout heroics, which will give him and the Liverpool fans confidence he can be an able deputy during Alisson’s absence.
Two defeats, but promising signs from Chelsea
Chelsea lost 4-0 at Manchester United on Sunday and while this was another defeat for the Blues and their new manager Frank Lampard, there were plenty of positives to be taken from Wednesday night’s performance.
Lampard fielded a young side at Old Trafford but turned to the older heads in his squad for this game. The added bit of experience and quality showed, particularly in a dominant first-half display.
N’Golo Kante was by far the best player on the pitch in the opening 45 minutes as he pulled the strings in midfield, while Giroud showed the clinical finishing that was absent for the Blues at the weekend.
Christian Pulisic also caught the eye on his first competitive start for Chelsea.
The 20-year-old American provided a creative spark, while his movement and vision had more than a hint of Eden Hazard about them.
One moment that caught the eye saw him run onto a through ball in the first half, cut inside before tucking a neat finish inside the near post. However, the goal was ruled out for offside following a VAR check.
If Lampard is able to get the balance of youth and experience right in his first XI, Chelsea could be an exciting team to watch this season.