Eduardo Da Silva's strike early in the second half was all Croatia needed to secure a 1-0 victory over Israel and move to the brink of qualifying for next year's European Championship.
The triumph for Slaven Bilic's side has left them with 26 points and kept them on top of Group E, three clear of England.
Russia have 18 points but have a game in hand.
Before a 35,000-strong crowd at the Maximir stadium in Zagreb, Croatia dominated from the start but failed to capitalise with numerous forays in the final third thwarted by Israel's last line of defense.
The Croats created, however, just one clear chance in first half and that was in the 15th minute when Leko's weak header finished at the feet of his team-mate, Ivica Olic.
Despite being just several yards from the goalline, his shot was stopped by goalkeeper Nir Davidovitch.
Still, the Croatians showed no signs of nervousness and they were finally rewarded for their hegemony shortly after half-time when Da Silva scored.
It happened in the 52nd minute when he connected with Vedran Corluka's precise cross from the right wing, with Da Silva's diving left-foot volley sending the ball past Davidovitch.
Both sides failed to show exciting football after crucial moment of the match, but still created two good chances in final half-hour.
Yossi Shai Benayoun's shot from the distance was stopped by Croatian goalkeeper Stipe Pletikosa.
Then Davidovich kept out Dario Srna's dangerous free-kick.
"This was a very tough match, without many chances, but the most import thing is that we've won," said Croatia captain Robert Kovac.
"We wanted three points from this clash, and we've got them. That's only important thing at the moment."
Kovac said he and the rest of Croatia will be England fans this week.
"On Wednesday, we'll be calm," he said. "We'll sit and watch TV, just like other fans from Croatia.
"And, at the moment Russia fail to defeat England, we'll start to celebrate. I think we've deserved that joy."
Copyright (c) Press Association
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