A fast start to the game from Liverpool saw January star signing Luis Diaz among the thick of the action, and the Colombian found himself clean through on goal with only nine minutes gone before Edouard Mendy thwarted him.
Marcos Alonso and Christian Pulisic threatened for the Blues but could not break down Alisson Becker in a goalless first half - one which saw Mohamed Salah's final cut short by an apparent muscular injury as the attacker hobbled off just after the half-hour mark.
Chelsea came flying out of the blocks in the second half, with Pulisic forcing a save out of Alisson before Alonso once again went close to breaking the deadlock - this time seeing a free kick come crashing back out off the crossbar.
Neither side were able to take their multitude of chances as the game entered its final knockings, although Andy Robertson must have thought he had won the cup for Liverpool before seeing his effort from a yard out cannon back off the post.
The two teams entered extra time as Virgil van Dijk trudged off to be replaced by Joel Matip, but with neither team able to make the breakthrough, the two sides would be separated by the dreaded spot-kicks again.
Liverpool now prepare to meet Southampton and Wolverhampton Wanderers before the Champions League final with Real Madrid on May 28, while Chelsea round off their Premier League campaign versus Leicester City and Watford.
4th min: An early mistake from Edouard Mendy gifts the ball back to Liverpool, but Thiago Alcantara just cannot get a foot on Luis Diaz's ball across for what would have been a certain opener.
9th min: Trent Alexander-Arnold plays a delightful outside-of-the-foot pass to Diaz, but Mendy's legs slow the momentum of the Colombian's shot before Trevoh Chalobah gets back to clear with the ball trickling closer to the goal.
23rd min: First real chance for Chelsea as Mason Mount finds Christian Pulisic in the box following a quick break, and the American's tame shot trickles centimetres wide of the far post.
33rd min: Mohamed Salah goes down in the Chelsea half with an injury and cannot carry on. Diogo Jota comes on for Liverpool.
45th min: Mateo Kovacic is dispossessed and Liverpool quickly break - Andy Robertson's cross finds the boot of Jota in plenty of space, but the Portuguese lifts his volley over Mendy and over the bar.
47th min: Pulisic now turns provider for Marcos Alonso, whose effort just flashes wide of the post before the former forces a save out of Alisson - fast start to the second period for the Blues.
48th min: Chelsea so close to breaking the deadlock again as Alonso's free kick from a tight angle beats Alisson and comes crashing back off the crossbar.
52nd min: A sharp turn from Diaz opens up the angle for a 20-yard effort - one which again clips the edge of the post before sailing out for a goal kick.
84th min: Mane plays in Diaz on the right-hand side, but it is frustration for the Liverpool man once again as his sliced effort strikes the outside of the post before Andy Robertson hits the other side of the woodwork from a yard out.
90th min: Diaz breaks away in the final few moments but his curling effort whiskers just wide of the post as the two sides go to extra time. Van Dijk is replaced by Matip for Liverpool.
107th min: Chelsea want a penalty as Hakim Ziyech goes down after an apparent tug back from Alexander-Arnold, but nothing is given. The contact was initiated outside of the box anyway.
Penalties Cesar Azpilicueta steps up and watches his penalty smash the post, but Mendy saves from Sadio Mane to force sudden death. Alisson then keeps out Mason Mount before Tsimikas slots home to spark jubliant Reds celebrations.
MAN OF THE MATCH - TRENT ALEXANDER-ARNOLD
As well as delivering one of the greatest passes an FA Cup final has ever seen for Diaz's early chance, Trent Alexander-Arnold was an imposing figure during the entire 120 minutes for the Reds.
The right-back's sumptuous outside-of-the-foot ball to Diaz was one of his four key passes on the day, while he also made four clearances and three tackles but could only watch his teammates squander their efforts in front of goal - he converted his penalty with panache, however.
Former Blue Mohamed Salah needed no added motivation to get one over his old club, but just like in the 2018 Champions League final, the Egyptian's game was cut short in the opening 45.
With no one else around him, the 29-year-old went down with an apparent muscular injury and had to be replaced by Diogo Jota - joining midfield enforcer Fabinho in the treatment room.
While the extent of Salah's damage is currently unclear, Liverpool fans will not rest easy ahead of his proposed revenge meeting with Real Madrid in Paris later this month.
Possession: Liverpool 53%%-47% Chelsea
Shots: Liverpool 17-10 Chelsea
Shots on target: Liverpool 2-2 Chelsea
Corners: Liverpool 5-5 Chelsea
Fouls: Liverpool 12-13 Chelsea
LIVERPOOL (4-3-3): Alisson; Alexander-Arnold, Konate, Van Dijk (Matip 90), Robertson (Tsimikas 111'); Thiago, Henderson, Keita (Milner 74'); Salah (Jota 33'), Mane, Diaz (Firmino 98')
CHELSEA (3-4-2-1): Mendy; Chalobah (Azpilicueta 105'), Silva, Rudiger; James, Jorginho, Kovacic (Kante 66'), Alonso; Mount, Pulisic (Loftus-Cheek 105', Barkley 119'); Lukaku (Ziyech 85')
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