Phil Neville scored the winning spot-kick after Nicolas Anelka and Ashley Cole both missed for the Blues, whose quest for a historic hat-trick of cup wins lay in tatters.
Chelsea wasted a hatful of chances to win the fourth-round replay in normal time and Frank Lampard finally gave them a 104th-minute lead but Leighton Baines levelled in the 119th minute with a brilliant free-kick.
The full-back missed Everton's first penalty in the shootout but it did not matter as the Toffees set up a last-16 tie with Reading.
Chelsea, who had not scored in their previous two games, were fortunate still to be in the competition after Kalou netted a late equaliser in last month's original tie.
They had not beaten Everton since the 2009 final and had won only one of their previous six home meetings with the Toffees.
Source: PA
Source: PA