Under Danish-born coach Thomas Christiansen, Panama have implemented a tight defensive structure that helped them secure their second-ever World Cup appearance.
But it was the Panamanian offence that almost made the difference in the first half.
In the 23rd minute, Jose Luis Rodriguez guided a header towards goal but the outstretched fingertips of Croatian goalkeeper Dominik Livakovic redirected the ball off the bar.
The second half marked a clear momentum shift and the capacity crowd of 43,000 in Toronto with a strong Croatian majority erupted when Budimir tapped in a cross from Josip Stanisic.
Croatia should have been two up minutes later, when a perfectly weighted pass from Modric sent Marco Pasalic alone speeding towards goal.
Pasalic’s first effort was stopped by keeper Orlando Mosquera and although the rebound came back to him he blasted an off-balance second attempt well over the bar.
Panama kept pressing for the equaliser but they ultimately failed to find the net, extending their World Cup goalless streak.
They face England next in what will be their final match of the tournament.
Croatia have three points and will next face Ghana, who moved onto four points and second place in Group L after holding England to a goalless draw earlier.
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