Ghana had already clinched a spot in the round of 32 for the first time since 2010.
Vlasic headed home Luka Modric's corner in the 83rd minute on Saturday (Sunday AEST) to score the winner and put Croatia back in contention after they finished third in 2022. The win means Croatia finished second behind England in Group L, with Ghana third.
Sucic scored in the 31st minute for Croatia on an absolute rocket from outside the box for his second career international goal.
Derrick Luckassen scored the equaliser that sent thousands of fans wearing yellow into a frenzy.
Luckassen found the bottom right corner in the 73rd minute to make it 1-1 and mark the first of the five group stage games in Philadelphia in which both teams had scored.
Vlasic scored the winner in the 83rd minute and wagged his tongue and ran toward his teammates with outstretched arms in celebration.
Sucic helped Croatia take a 1-0 lead into halftime in a game in which a couple of near misses prevented them from building a more comfortable lead.
Ghana seemed poised to level the game late in the half when Antoine Semenyo beat his man and fired a shot that went just wide of the left post.
Semenyo was one of the few prominent attackers in this tournament to go without a goal in the first three games.
He finished third in the Premier League with 17 goals last season and was one of Manchester City's best players after they bought him from Bournemouth, yet he couldn't connect in the World up against Panama, England or Croatia's backline.
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