They were gifted what proved to be a fourth-minute winner when Luca Modric drilled home a penalty after Rene Aufhauser clumsily felled Ivica Olic.
Austria's Joachim Standfest headed their best chance wide as they finished the first half in better form.
And after the break Austria's Umit Korkmaz had a stinging shot well saved and Roman Kienast headed narrowly wide.
An equaliser would not have flattered a plucky Austria side who had to dig deep to recover from a terrible opening spell.
Croatia coach Slaven Bilic said afterwards: "Some players were overwhelmed by playing at a great tournament but we started off with the best possible way - with a win.
"In the first 35 minutes we played excellently, of course the early lead contributed to that.
"They exerted more pressure in the second half and I'm sure that is not to do with a lack of strength from our players. But we confined ourselves to our penalty area too early.
"The last 15 minutes or so when they play all or nothing, you can do that - but we started in the 60th minute or so."