Rakitic returned the favor moments later with Rustu left scrambling as Olic's header looped wide.
The wasted opportunity was put into sharp focus after 14 minutes when another breakaway saw Ivica Olic double Croatia's lead.
The striker was clearly standing in an offside position when he nodded in after Ivica Olic headed the ball on.
Rustu was again called into action as Modric crossed for Olic, but it was the last significant action in regulation play.
Thomas Muller put Bayern ahead in the 19th minute and Croatian Ivica Olic added the second two minutes after the break.
Then Carson partially atoned for his earlier error with a fine save from point-blank range to keep out a header from Olic.
Just before the interval Carvalho's speed and persistence provided him with room to maneouvre and he intelligently freed Ivica Olic on the right.
First Bridge was relieved when his attempted clearance under pressure from Olic went over the head of Carson and clipped the top of the crossbar.
Turkey were offering no attacking threat and another great chance fell to Rakitic who played a neat one-two with Olic only to blaze over under pressure.
England went 2-0 down when Scott Carson, in for Paul Robinson, fumbled Nico Kranjcar's shot into the net and then Ivica Olic slipped in a second.
Germany striker Klose failed to impress in his first start this season, and was replaced by Croatia's Ivica Olic -- who soon tested Bremen keeper Tim Wiese.
Croatia looked the more menacing and 35-year-old Turkish keeper Rustu had to be sharp to get ahead of Olic from a cross by the ever dangerous Rakitic.
Robben missed a penalty following Drogba's clumsy foul on Ribery, and Ivica Olic saw a shot roll agonizingly wide before Gomez smacked a shot into the post.
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England were again fortunate when Olic got the better of Bridge but this time Carson was able to cling on to his low drive away to his right.
Eduardo da Silva made a weaving run to the edge of the England box and the Arsenal player timed his pass to perfection as Olic beat the offside trap.
Ivica Olic scored the only goal of the game in the 62nd minute, stroking the ball into the empty net after keeper Nir Davidovic parried Mario Gomez's 20-yard strike into his path.
The second half was barely five minutes old when Olic came close again as he headed over Rustu and after sloppy defending had a second chance which was hacked off the line.
With time running out Robben's drive forced a good save from Sebastien Frey and when Olic headed the rebound on to Klose to nod home he was at least two yards offside.
Eduardo drove at the heart of the England defence and played a cute pass into the area for Olic, the Hamburg striker coolly dribbling round a shell-shocked Carson and rolling into an empty net.
England seemed keen to gift Croatia another goal as first Bridge cleared on to the top of his own crossbar and then Carson repaired some of the damage by brilliantly saving Olic's point-blank header.
But Olic and Schweinsteiger both missed their kicks.
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Wiese then denied Ribery, who set up Olic for another chance that the former Hamburg forward squandered, but the breakthrough came as Gomez stuck out a leg to just beat the goalkeeper to Phillip Lahm's cross and divert the ball into the net.
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