The sides, meeting in a second domestic cup final this season, played out an entertaining goalless draw over 120 minutes before being decided on penalties again.
Liverpool were on top in the early stages with Luis Diaz a particular threat. A through-ball from Trent Alexander-Arnold put Diaz through on goal in the eighth minute but Edouard Mendy denied him before Naby Keita put the rebound wide.
Chelsea made the faster start after the break with Pulisic drawing a save from Alisson and Alonso striking the crossbar from a free kick but both sides toiled and could only create half-chances for much of the second period.
Neither side were able to find a breakthrough in the additional 30 minutes, meaning spot kicks for the second time this season.