Substitute Ante Budimir supplied the decisive touch, grabbing the only goal early in the second half on Tuesday (Wednesday AEST) in Toronto as Panama's hopes of qualification were ended.
A tight first half produced few openings, Croatia goalkeeper Dominik Livakovic stretching to tip Jose Luis Rodriguez's header onto the bar although the ball was adjudged to have crossed the line before Amir Murillo's cross.
Croatia enjoyed plenty of possession, but uncharacteristically gave it away and allowed the Central Americans to look threatening on the break with Murillo making a dangerous run into the box.
The first shot on target arrived in the first minute of first-half added time, Orlando Mosquera turning Martin Baturina's low drive from 25 yards around the post.
Their next opening nine minutes into the second half proved decisive, Josip Stanisic delivering a wonderful cross which Budimir steered in at the far post.
A through ball from Modric released Marco Pasalic from halfway as Croatia broke from a Panama corner, but Mosquera stood tall and the striker was unable to turn in the rebound from a tight angle.
Livakovic made two quick saves from Murillo and pushed Carlos Harvey's header over the bar as Panama pressed for an equaliser, but their efforts petered out as Croatia were able to see out the victory.
Group L will be decided on Saturday, with England and Ghana tied on four points and Croatia with three. England will face Los Canaleros in New Jersey, while Ghana and Croatia will play in Philadelphia.
With the AP.
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