Goals from Corluka, Kalinic and Vukojevic sealed a comfortable victory over Tarmo Ruutli's men
A quickfire double from Vedran Corluka and Nikola Kalinic saw the hosts power into a first half lead. After a second half which was punctuated by a steady flow of substitutions, Ognjen Vukojevic made it 3-0 with nine minutes to go before Amkar Perm's Konstantin Vassiljev grabbed a late consolation as Croatia wrapped up an easy victory.
Slaven Bilic opted to use the international friendly to test a few inexperienced players named in his preliminary squad. The likes of Ivo Ilicevic, Milan Badelj, goalkeeper Danijel Subasic and substitute Sime Vrsaljko given time to stake their claims, with a few seasoned internationals also on show.
Estonia, who missed out on Euro 2012 with a play-off defeat to the Republic of Ireland, who are incidentally, Croatia's first opponents in Group C, began proceedings in lethargic form. The hosts dominated the early stages, though they themselves almost took a shock lead with Oliver Konsa's effort narrowly flying over the bar.
However, it was to be the only high point on a disappointing first half from Tarmo Ruutli's men. Eduardo lead the line magnificently in the first half and he came mightily close, but for the exploits of Sergei Pareiko between the sticks.
The hosts continued to surge forward at will, stringing move after move together, and not before long, they got their just reward from a free kick. Corluka was at the right place at the right time, putting the crucial touch past the Estonian custodian.
Croatia were in no mood to stop there. Perisic then came closest with a spectacular overhead kick which whistled just wide of the post. As unfortunate as the Borussia Dortmund man was, the Croats doubled their lead shortly after.
Kaarel Kidron was criminally dispossessed near the Estonia goal, allowing Eduardo to take control of the situation with a delightful backheeled pass into Perisic, and then into Kalinic, who made it 2-0 for the remainder of the first period.
The second half brought a steady flow of changes as Bilic tinkered with his side, and that provided the visitors to test Monaco's Subasic in the opposing goal. Despite their best efforts, only a Vassiljev free-kick came close to troubling the goalkeeper as a resolute defence largely held sway.
Towards the end, the match saw further goal action. Mario Mandzukic delivered a sting effort from inside the box which was well parried by Pareiko. Vukojevic tripled the advantage on 81 mins to make it 3-0 but Estonia scored a late consolation through Vassiljev's 14th international goal, but to no avail.
Croatia continue their preparations with a friendly against Norway next Friday, before their Group C opener against Giovanni Trapattoni's Ireland in Poznan on June 10.