Blackburn Rovers missed two second-half penalties before Everton's Mikel Arteta converted a last minute spot-kick for the visitors to seal all three points at Ewood Park.
Mauro Formica earned the first penalty for the home side shortly after the interval, following an unfair challenge by Ross Barkley. However, Tim Howard saved David Hoilett's shot to keep the sides on level terms.
Rovers were awarded their second spot-kick with 10 minutes to go, after Everton defender Phil Jagielka was adjudged to have fouled Formica. The Argentine took the set-piece himself, but sent his shot wide.
In the final minutes, the referee awarded Everton the controversial third spot-kick of the afternoon, when Christopher Samba was deemed to have fouled Marouane Fellaini. Spaniard Mikel Arteta hit the back of the net to win the game.
The victory is the Toffees' first of the season, while Blackburn are yet to get off the mark after three games.