Van Dijk had seen a header contentiously ruled out for offside on the hour but there was no reprieve for Chelsea when he glanced home another from Kostas Tsimikas' corner in the 118th minute.
Liverpool's 10th triumph in the competition was achieved without a host of injured star names, including forward trio Mohamed Salah, Darwin Nunez and Diogo Jota, also losing Ryan Gravenberch when he was taken off on a stretcher after Moises Caicedo's first-half challenge.
It means Jurgen Klopp's side have achieved the first part of a potential four-trophy haul in the manager's farewell season, but it was a bitter blow to Chelsea and manager Mauricio Pochettino.
They have now lost six successive Wembley finals, including three against Liverpool, and wasted a host of opportunities here.
Liverpool were indebted to goalkeeper Caoimhin Kelleher who produced another outstanding Wembley performance after being the hero when Chelsea were beaten on penalties in the 2022 EFL Cup final.
In a tight first half, he blocked brilliantly from Cole Palmer while Liverpool's Cody Gakpo saw a header bounce back off the post. Chelsea's Raheem Sterling also saw a close-range effort ruled out for offside against Nicolas Jackson.
As the chances came thick and fast after the break, Van Dijk thought he had headed Liverpool in front on the hour only for the goal to be contentiously ruled out for offside against Wataru Endo following a lengthy Video Assistant Referee (VAR) intervention as the Japan midfielder blocked off Chelsea defender Levi Colwill.
Conor Gallagher was also denied by the woodwork, then once more by the defiant Kelleher as he looked poised to make the breakthrough, Liverpool's keeper darting off his line to save while Chelsea somehow failed to score in a desperate goalmouth scramble in the closing moments of normal time.
Kelleher's Chelsea counterpart Djordje Petrovic was called into action in extra time, turning over a header from Liverpool's teenage substitute Jayden Danns while Harvey Elliott shot into the side-netting from a good position, also seeing a header miraculously kept out by the keeper.
And then came that final twist to give Liverpool another Wembley victory over Chelsea and leave Pochettino still seeking his first trophy in England.
The odds on Liverpool securing another Wembley win lengthened when the teamsheet landed and the names of Salah and Nunez were added to other high-profile absentees Trent Alexander-Arnold, Jota and keeper Alisson.
And yet, once more, Liverpool overcame this handicap, Klopp trusting Liverpool's emerging youngsters in a major final as three rookies were sent into the Wembley fray as substitutes in the shape of 19-year-old duo Bobby Clark and James McConnell, along with 18-year-old Danns.
All three showed remarkable composure in the heat of battle, offering further evidence of Liverpool's bright future after Klopp departs in the summer.
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