Croatia, who will feature in the tournament's opener against hosts Brazil on June 12, were not at their fluent best but showed glimpses of their undoubted quality at the Stadion Gradski.
Perisic got their opener when he finished a clever ball from Ivan Rakitic after 15 minutes and he wrapped up an impressive performance with a second four minutes after the hour.
His close-range finish from Ivica Olic's knockdown helped settle any Croatian nerves but coach Niko Kovac will have been disappointed to see Cheick Diarra take the shine off their performance - heading home from a corner late on.
Former Croatia international Kovac will hope to see a more complete display when his side take on fellow World Cup hopefuls Australia on June 7.
He named Luka Modric and Nikica Jelavic on the bench for the first of the Europeans' pre-World Cup friendlies and they got off to a strong start when Perisic fired home the opener early on. With 15 minutes on the clock, the impressive Rakitic slid through a well-executed pass for his team-mate, who clipped the ball home with the outside of his right foot.
The duo almost combined again shortly afterwards when the Sevilla star chipped over a ball for the onrushing Wolfsburg man, only for it to be partially cleared.
Perisic almost got a second chance when Mahamadou N'Diaye and Tongo Doumbia failed to properly deal with the delivery but Soumbeila Diakite was able to produce a stop.
The visitors began the second half well and caused the Croatian defence problems in the air but their opponents' speed and technical quality was soon on show again.
Substitute Sime Vrsaljko saw a shot well saved after a quick break and, after Olic had got his head on Rakitic's resulting corner, Perisic was able to prod home the second.
Nouha Dicko flashed a strike just over the crossbar for Mali before Kovac opted to withdraw Mario Mandzukic, Perisic and Rakitic.
Jelavic, Modric and Eduardo da Silva were also given brief run-outs, with substitute Diarra's consolation proving Croatia's only low point.