The scoreline -- identical to Brazil's nightmare 7-1 defeat by Germany in the World Cup semi-final two years ago -- takes Brazil to the top of Group B with four points, ahead of the evening's second game between Peru and Ecuador.
Coutinho got Brazil off to a positive start in the Camping World stadium with a goal after 14 minutes when he skipped past a defender and hammered home from 20 metres out.
He doubled Brazil's lead 15 minutes later thanks to Jonas, who was on hand to poke a loose ball across goal and leave the Liverpool player with the simplest of tap-ins.
Renato Augusto made it three in 35 minutes when he rose unmarked to head home a cross from the right.
Although the eight-times Copa America champions appeared to take their foot off the pedal in the second half, they still created chances at will against 74th-ranked Haiti.
Gabriel scored the fourth just 13 minutes after replacing Jonas at half-time and his Santos team mate Lucas Lima nodded home a Dani Alves cross eight minutes later.
Haitian striker Marcelin delighted the Caribbean contingent in the Orlando crowd by hammering in a rebound but Renato Augusto restored Brazil's five-goal advantage when he seized on a loose pass and side-footed home from 20 metres.
Coutinho completed his hat trick in the final minute of injury time with a trademark 25-metre strike.
Brazil, who were held 0-0 by Ecuador in their opener, next face Peru on Sunday. Haiti, who also lost their opener to Peru 1-0, will take on Ecuador.
(Writing by Andrew Downie; Editing by Ian Ransom)
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