Kranjcar double defeats Israel
Kranjcar scored from the penalty spot in the 36th minute and added his second four minutes before the break with an excellent low shot.
Etay Shechter pulled a goal back for the hosts nine minutes from time to set up a tense finale but Croatia held firm despite late pressure.
Croatia have seven points from three games with Georgia and Greece on five. Israel have four followed by Latvia (3) and Malta (0).
"I am happy and proud of my players... we caught Israel on the break five or seven times and we almost scored a third goal to kill the game, but once Israel scored there was a dangerous time for us at the end," said Croatia coach Slavan Bilic.
"It was a very exciting game to watch, Israel had some early chances when we made some technical errors but we took control later on and played our normal game, controlling mainly on the right side... Israel let go of the ball in very dangerous areas," he added.
The Croatians had to contend with a new-look Israel side that included a number of young players and missing captain and mainstay Yossi Benayoun, who has was ruled out through injury.
Shechter tested Croatia goalkeeper Vedran Runje with an early strike but the hosts had a let off when Ivan Rakatic struck the post with a powerful strike from 25 metres.
Croatia looked the more dangerous side as the teams began to settle down but the Israelis recovered their composure and found a way through the visitors' defences a number of times, although they could not find a way past Runje in goal.
The Croatians, who mainly exploited space on their right with Ivica Olic making forays into the area, finally got the breakthrough when defender Dekel Keinan fouled Josip Simunic to concede a penalty which Kranjcar blasted past Dudu Aouate.
He quickly struck again from close range when he latched onto a cross from the right by Luka Modric.
It was a second straight victory for Croatia over Israel at their home headquarters in Tel Aviv where they rarely lose. In November 2006 the visitors enjoyed a 4-3 win in a Euro 2008 qualifier.
Asked why Israel should have lost again, Bilic said:
"I think you (Israel) suit us in the way you play. Israel like to play football as much as we do and when they give us space we are dangerous."
Israel coach Luis Fernandez said Benayoun's absence had been a big blow for his side, although he thought his players had played well.
"Benayoun is always important for us but the Croats also missed players but I am not upset, I liked the attitude. We started very well, we had some good early chances but after they scored the penalty and we conceded another goal soon afterwards it was very difficult," the Frenchman said.
Israel will miss another vital player for their next qualifier, away to Greece on Tuesday after central defender Tal Ben Haim was booked and will serve a one-match suspension.