New Zealand came out with extra vigour in the second half and both Howieson and Boyd tested Sluga in the Croatian goal.
The introduction of Ante Rebic for Croatia was to prove decisive as the striker picked up the ball on the edge of the area and fired the ball into the top corner on the 75th minute.
The Junior All Whites rallied and Boyd almost scored a spectacular volley before Fenton turned sharply into the box forcing a save from Sluga. It was substitute Fenton that would earn the penalty and score to give New Zealand their first goal of the tournament.
Croatia would finish the game strongest with Miskic striking the crossbar with a long range shot.
The victory for Croatia gave them top spot in the group with Uruguay second and Uzbekistan reaching the next round as one of the best third-placed teams.
Croatia 2 (Stipe Perica 11, Ante Rebic 75) New Zealand 1 (Louis Fenton 84) HT: 1-0