Kramaric produced a superb all-round performance after coming on as a halftime substitute, injecting life into a toothless Croatian side, which fell behind to an Ismaila Sarr goal in the 48th minute.
Winger Ivan Perisic equalised with a heavily deflected free kick before Kramaric showed a killer instinct in the penalty area, drilling in a rebound after a Senegalese defender blocked his first shot.
The Croatians open their Group D campaign against Nigeria on June 16 before taking on Argentina and Iceland, while Senegal play Poland on June 19 in Group H followed by games against Japan and Colombia.
Croatia dominated possession in the first half but their ineffective 4-2-3-1 formation, with Mario Mandzukic as the lone striker, created no clear cut chances while Senegal always looked dangerous on the break.
The visitors silenced a packed and passionate home crowd in Osijek as Sarr latched on to a delightful long ball by Alfred N'Diaye from the halfway line and steered it past goalkeeper Danijel Subasic.
Lively Kramaric, whose running enabled Croatia to move up a gear, shaved the crossbar before Perisic levelled from 30 metres as the ball struck a defender in the Senegalese wall and left goalkeeper Abdoulaye Diallo wrong-footed.
The fired-up Croatians kept the visitors on the back foot and Kramaric deservedly grabbed the winner when he drove a left-footed rebound into the bottom corner after a delightful through ball by captain Luka Modric.
Sadio Mane, who gave Croatia's defenders a torrid time all evening with his pace and trickery, missed Senegal's last chance to salvage a draw as he rattled the woodwork with a free kick.
(Writing by Zoran Milosavljevic in Belgrade; Editing by Toby Davis)
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