The hosts, who had won all of their previous four fixtures, appeared fortunate not to give away a penalty in the first half as clumsy challenges in the box by Glenn Whelan and Stephen Kelly went unpunished.
They nearly broke the deadlock soon after when Shane Long saw his header kept out by goalkeeper Stipe Pletikosa, though, while Richard Dunne missed their best chance after the break.
Although a string of players had withdrawn from his squad due to injury in the build-up to the match, Ireland boss Giovanni Trapattoni was able to name a relatively strong first XI.
In the absence of striker Kevin Doyle, who had become the latest withdrawal a day earlier, it was captain Robbie Keane and new West Brom signing Long leading the line in a side which also featured the likes of Shay Given, Dunne and Damien Duff.
The Republic were looking to keep up their recent momentum ahead of their Euro 2012 qualifying double-header against Slovakia and Russia next month with a positive performance against the Croatians, whose starting line-up included Tottenham trio Luka Modric, Niko Kranjcar and Vedran Corluka.
Given that sort of star quality and the fact that Slaven Bilic's team are ranked ninth in the world, Trapattoni will view this as another encouraging result for his charges.
The first chance of the contest fell to Stephen Hunt, whose miscued volley sent the ball harmlessly wide, and Darron Gibson shot straight at Pletikosa shortly after having been fed by Duff.
It was the visitors who then began to get forward, though, with Darijo Srna delivering a cross that was just too high for Kranjcar and a corner which former Arsenal frontman Eduardo connected with, only to see his effort blocked by Long.
Whelan appeared to bundle Eduardo over in the area in the 13th minute but referee Tom Harold Hagen allowed play to continue, and Croatia certainly felt they deserved a penalty moments later when Ivan Strinic fell under the attentions of Kelly, yet the outcome was the same.
At the other end, Long went close as he headed Whelan's cross goalwards, Pletikosa getting down to make the save.
Kranjcar fired over wildly from distance and Given claimed a ball floated into the danger zone by Srna.
Long evaded his marker to race on to a pass but Dejan Lovren put the ball behind for a corner, which Sean St Ledger met but could only divert off-target.
Kranjcar ballooned over again after getting on the end of Srna's low delivery, but Ireland finished the opening period strongly.
Keane stabbed a shot at Pletikosa having jinked into the box before St Ledger headed a corner wide.
Modric tried something spectacular nine minutes after the restart but sliced his acrobatic effort.
Gibson then picked up a booking for a robust tackle on Ivica Olic, who had been introduced at the interval for Eduardo.
Srna sent a free-kick across the Ireland area which Lovren hit the wrong side of the far post, and Croatia continued to press, with Mario Mandzukic putting the ball wide after his initial effort had bounced back off Hunt.
Trapattoni then made a double substitution, bringing on Andy Keogh and Kieren Westwood for Hunt and Given.
Dunne was presented with what seemed a glorious opportunity with around 20 minutes to go when St Ledger crossed into the box, but having risen to connect with the ball, the Aston Villa defender was unable to direct his header towards goal.
Darren O'Dea was next to come on in place of Whelan, before Srna struck just wide.
With Simon Cox and Keith Treacy having then replaced Long and Duff, Westwood kept out a shot by Croatia substitute Nikola Kalinic five minutes from the end as the Republic held on.