In a game devoid of clear-cut opportunities David Marshall made the game’s best save in final seconds of the first-half.
The 28-year-old reacted quickly to palm away a deflected header from Nikica Jelavic, with Cardiff also lucky to survive to good penalty claims.
Both Roberto Martinez and Malky Mackay named unchanged sides from their opening Premier League outings, as Fraizer Campbell continued up front for Cardiff and Ross Barkley lined up in support of Jelavic for the visitors.
Marouane Fellaini and Leighton Baines both started once again, despite continued reports linking the pair with moves to Manchester United.
Peter Whittingham had the first chance of the game as he sent an inswinging corner towards the front post and Tim Howard was forced to come through a crowd of players to claw the ball away.
Everton slowly came back into the game and felt they should have had a penalty in the closing five minutes of the half.
Leighton Baines charged into the penalty area and was challenged by Gary Medel only for referee Anthony Taylor to award a goal kick.
Marshall then kept his side in the half with an instinctive save from a Jelavic header in stoppage time.
The Croatia international met a Seamus Coleman cross strongly, only for the goalkeeper to react brilliantly and deny the striker after his effort had taken a deflection off Ben Turner's arm, with further Everton penalty appeals falling on deaf ears.
The 28-year-old should have opened the scoring for the visitors seven minutes after the break, however he blazed over the crossbar after a neat through ball from Fellaini.
Martinez introduced Arouna Kone for Jelavic just after the hour, and the Ivorian had a fantastic chance to win the game in the closing 10 minutes.
He reacted quickly to volley a shot towards goal after a scramble in the penalty area, Marshall saved well but Kone was flagged offside.
Baines and Fellaini combined on the edge of the penalty soon after but the full-back's right-foot shot skewed high and wide of goal as the game petered out into a dull draw.
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