The former West Ham keeper marked his full competitive debut for the Reds with a decisive save to deny Tammy Abraham after the first nine spot-kicks were all converted.
Jurgen Klopp's Champions League winners were second best for much of the first half and deservedly went in at the break trailing to Olivier Giroud's well-taken strike.
The Reds responded by bringing Roberto Firmino off the bench from the restart and the Brazilian forward made an instant impact, teeing up Sadio Mane for a simple tap-in three minutes later.
Liverpool looked a completely different proposition with their front three back in tandem and they moved ahead five minutes into extra time. Once again Firmino turned provided for Mane to flash a stunning strike into the top corner.
However, Chelsea hit back soon after as Adrian was controversially penalised for bringing down Abraham in the area. Jorginho stepped up to level and send the match to a shoot-out.
Next up, Liverpool visit Southampton in the Premier League on Saturday while Chelsea will hope to pick up their first competitive win under Lampard at home to Leicester on Sunday afternoon.
Liverpool survive VAR controversy to win another trophy for Klopp, while there are still plenty of positives in defeat for Lampard.
The Merseysiders were left frustrated when Stéphanie Frappart, who became the first female to take charge of a major European men's final, awarded Chelsea a spot kick in extra time. Adrian was penalised for catching Abraham as he chased a loose ball in the area. Replays were inconclusive and yet there was no intervention from VAR. At that point, Adrian was the villain, but recovered to make the crucial save in the shoot-out. The Spanish stopper has had a whirlwind couple of weeks and, overall, will be pleased with his contribution after replacing the injured Alisson to help the Reds win a second trophy under Klopp.
As for Chelsea, there were some questions marks over Lampard's tactics and team selection in the Blues' 4-0 humbling at Manchester United, but he got a hugely positive response from his side here. N'Golo Kante made a real difference after shrugging off injury to start and despite the shoot-out loss, Chelsea gave a very strong account of themselves against the European champions that bodes well going forward.
MAN OF THE MATCH
Sadio Mane (Liverpool). The Senegal man has barely had a rest over the summer, but you wouldn't know it as he made a huge contribution in attack. Firmino and Kante ran him close in a high quality encounter.
LIVERPOOL: Adrian 7, Gomez 7, Matip 7, Van Dijk 7, Robertson 6, Fabinho 7, Milner 7, Henderson 7, Oxlade-Chamberlain 6, Mane 9, Salah 7. Subs: Firmino 8, Wijnaldum 6, Alexander-Arnold 6, Origi 6.
16' - LIVERPOOL CHANCE! The first real chance of the match falls for Salah. The Egyptian surges free onto the Ox's pass and runs into the area from the right but sees his low effort well saved by Kepa.
22' - CHELSEA CHANCE! Pedro plays a one-two with Giroud and races into the left side of the box before seeing his rising shot cannon back off the crossbar.
34' - CHELSEA CHANCE! Pedro with a delightful pass for Kovacic, who races clear on Adrian but can't find a way beyond the Liverpool stopper. Super save.
36' - GOAL! Liverpool 0-1 Chelsea. The Europa League winners lead. Giroud is given too much space to surge into the left of the area and coolly fire Pulisic's pass beyond Adrian.
48' - GOAL! Liverpool 1-1 Chelsea. Liverpool pull level. Firmino makes an immediate impact, prodding a lovely touch past Kepa to set up Mane for a simple tap-in after the forward had reacted first to Fabinho's lofted pass over the top.
75' - LIVERPOOL CHANCES! What a double save! Salah sees his low shot pushed out by Kepa, who then gets up to tip van Dijk's close-range follow up against the crossbar! So close for Liverpool.
95' - GOAL! Liverpool 2-1 Chelsea. Mane thunders a stunning shot into the top corner after playing a neat one-two with Firmino down the left.
101' - GOAL! Liverpool 2-2 Chelsea. Jorginho fools Adrian with a little skip before rolling his penalty the opposite way to the keeper's dive. The spot-kick was awarded after Adrian was penalised for catching Abraham.
105' - CHELSEA CHANCE! It should be 3-2 to Chelsea. Pedro cuts it back from the right for Abraham who somehow steers wide from close range.
SHOOT-OUT' - SAVE! Liverpool 5-4 Chelsea. Adrian makes the decisive save from Abraham to win the cup for the Reds after the first nine penalties were all converted.
Giroud has 12 goals in his last 13 UEFA club competition appearances.
Mane has scored 19 goals for Liverpool in all competitions in 2019. That's at least seven more than any other Reds player (Salah 12). Only Sergio Aguero (20) has notched more for a Premier League side.
Mane is the first African player to score in the UEFA Super Cup since Frederic Kanoute notched for Sevilla v Barcelona in 2006.
Only Barcelona and Sevilla (4 each) have been runners-up in the UEFA Super Cup more often than Chelsea (3)
Only Barcelona and AC Milan (5) have won the UEFA Super Cup more often than Liverpool (4 - 1977, 2001, 2005 and 2019).