Third-place Liverpool, now winless in four games, could only gain one point Tuesday night against its Merseyside rivals. The Reds are nine points behind Premier League leader Blackburn but have played one more game than the Rovers.
In other Premier League games, Leeds routed Queens Park Rangers 4-0 and Arsenal and Southampton drew 1-1.
Liverpool held most of the possession against Everton, yet the visitors had two of the better scoring chances late in the game. Midfielder Barry Horne's drive was just wide after going through a crowd of players, and Paul Rideout's volley was saved by Liverpool goalkeeper David James.
At Leeds, Phil Masinga scored twice to give the South African five goals in his last two games.
Masinga, who had a hat trick last week against Walsall in the FA Cup, netted in the 31st and 60th minutes. David White, in the 33rd, and Brian Deane in the 84th also scored for Leeds.
At Arsenal, new signee John Hartson scored the first goal of the match when he headed home the rebound after goalkeeper Bruce Grobelaar pushed away Ian Wright's lob in the 21st minute. Southampton tied it on Jim Magilton's goal in the 74th with an assist from Matthew Le Tissier.
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