Nikica Jelavic's opportunist 68th-minute header got Igor Stimac's reign as Croatia coach off to a winning start against FYR Macedonia in Group A.
The Everton striker headed into the bottom corner of the net from close range after connecting with an Ivan Perisic cross to seal the points for the hosts, who were made to battle for their victory by a dogged Macedonian line-up.
Stimac's men had got off to a good start with Eduardo firing against the post with less than two minutes on the clock then a dangerous Mario Mandzukic cross booted clear by alert Macedonian defender Nikolce Noveski.
Macedonia had their moments, with Agim Ibraimi's set-pieces causing problems and Vance Sikov coming close with a header on the half-hour which was cleared from deep by Darijo Srna.
Perisic headed wide for Croatia five minutes later, but Macedonia were close to snatching a shock half-time lead four minutes before the break when Goran Pandev's 20-yard effort struck the bar.
Half-time substitute Niko Kranjcar added momentum to the Croatian attacks early in the second period, but it was Jelavic's introduction in place of Eduardo in the 58th minute which made the crucial difference.
Jelavic's goal looked to have settled Croatian nerves but Macedonia still pressed for an equaliser and a Darko Tasevski free-kick caused some problems in the home box before it was cleared by Josip Simunic.
Having been reprieved, Stimac's men saw out the remainder of the match with the minimum of fuss, with Srna bringing a good save out of Martin Bogatinov as he looked to double the margin of victory before the final whistle.