The Liverpool player was in top form and opened the scoring in the 14th minute.
He doubled the lead with a tap-in, before Renato Augusto headed home from an inch-perfect Dani Alves cross from the right wing.
Brazil led 3-0 lead at half-time at the Camping World Stadium.
Brazil coach Dunga replaced Jonas Oliveira with Gabriel in attack before the start of the second-half.
And the 19-year-old - dubbed the new Neymar - scored in the 59th minute.
Lucas Lima, another substitute, headed home to make it 5-0.
Haiti then had something to celebrate as James Marcelin scored the nation's first goal of the 2016 Copa America.
Brazil then completed the rout as Augusto scored again and Coutinho completed his hat-trick with a fine solo effort.
It was Brazil's first win of the tournament after drawing their opening group game 0-0 against Ecuador.
Haiti became the first team to be eliminated from the tournament, They lost 0-1 to Peru in their opening match.