Liverpool kept alive hopes of an unprecedented quadruple as Konstantinos Tsimikas struck a sudden-death penalty winner to earn victory over Chelsea in the FA Cup final.
Liverpool dominated the first half of the game, with Luis Daz posing a particular menace on the left flank. After being put free by a superb curling ball from Alexander-Arnold, the Colombian was denied in the eighth minute as his effort was expertly stopped by Édouard Mendy, with Nathan Chalobah scrambling the rebound away off the line under pressure from Mo Salah.
After Christian Pulisic was set up by Mount, Chelsea began to settle, and Alonso had the finest chance of the first half-hour after Pulisic slid a pass to him on the left in the 28th minute, but Alisson saved his low near-post attempt.
Salah went down with a groin injury five minutes later, and he was replaced by Diogo Jota, who squandered Liverpool's finest chance of the half when he glanced a close-range volley over from Andy Robertson's left-wing cross.
Chelsea had a flurry of chances in the second half, with Alonso hitting barely wide from the left after Pulisic found space on the right. Alonso struck the crossbar with an inswinging free-kick on the right after Alisson turned away a powerful drive from the American.
After being played in by Naby Keta, Liverpool responded with Diaz shooting barely wide from distance and Jota thumping a shot just past the post.
After a tempting cross from replacement Milner, Jürgen Klopp's team had perhaps the finest chance of the second half when Robertson slammed the post from close range. Although Liverpool ended well, as they did in the Carabao Cup final in February, a goalless 90 minutes prompted extra time.
Chelsea started the additional half-hour better and were almost awarded a penalty early in extra time after substitute Ziyech was brought down by Ibrahima Konaté's reckless shoulder charge, but referee Craig Pawson turned them down.
Both sides were fatigued, and penalties seemed to be looming.
After César Azpilicueta struck the post with the second Blues spot-kick, Sadio Mané squandered the chance to win it with a feeble fifth effort, and Liverpool held the edge in the shootout.
Mason Mount, though, missed Chelsea's seventh kick, allowing Tsimikas to score the game-winner and keep Liverpool's dreams of a quadruple alive.
Chelsea's goals came from Marcus Alonso, Reece James, Ross Barkley, Jorginho, and Hakim Ziyech, while Liverpool's goals came from James Milner, Thiago Alcântara, Roberto Firmino, and Trent Alexander-Arnold.