Roberto Martinez's side had a strong appeal rejected but could only achieve its third draw in a row as Malky Mackay's men held on to earn a point at the Cardiff City Stadium
In a game devoid of clear-cut opportunities, David Marshall made the game’s best save in the final seconds of the first half, the 28-year-old reacting quickly to palm away a deflected header from Nikica Jelavic, with Cardiff also lucky to survive two good penalty claims.
Marouane Fellaini and Leighton Baines both started once again for Everton, 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, however, and felt it 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.
And 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 experienced 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, though he blazed over the cross bar 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, although Marshall saved well and 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 - Martinez's third in three league games as Everton boss.