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.
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.
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.
