Chelsea's hopes of finishing among the Premier League's top four were hurt after they lost 2-0 to Everton at Goodison Park on Sunday.
Richarlison scored in back-to-back league games for the first time since December as he headed in the opener. Gylfi Sigurdsson converted from the spot after Marcos Alonso fouled Richarlison in the box, giving the Toffees their second win in four league games to move up to 11th.
Maurizio Sarri's side remain sixth in the standings and one point behind Manchester United, who were knocked out of the FA Cup quarter-finals following a 2-1 defeat at Wolverhampton Wanderers on Sunday.