Winning the battle is (somewhat) simple, the Brazilian Army left the field but the Uruguayans and Argentinians were too exhausted(after 11 hours of fighting) to follow it(or do anything else than occupy the field), with parts of their army crumbling by the end of the Battle just as in the Brazilian Army(that's why the Brazilians say the battle was a tactical draw while Uruguayans and Argentinians say it's a victory). So what the Brazilians had to do was to stay on the field a bit longer, which may have been possible or not.
As for it being enough to win the war, it wasn't. Brazil already had control of the coastal cities of Uruguay, what Ituzaingó/Passo do Rosário did was confirm Brazil didn't have control of the Uruguayan interior(and Brazil didn't have it since at least the Battle of Sarandí). What could win the war(and was winning it) for Brazil was the Buenos Aires blockade, which never was really threatened(the last effective try to threaten the blockade ended in Argentinian defeat, nearly two months after Ituzaingó/Passo do Rosário - the Battle of Monte Santiago).
In the end, Ituzaingó/Passo do Rosário doesn't mean that much. If Brazil could have extended the blockade up to late 1828, it would win, no matter how many battles in the interior Brazil loses(the Brazilian Navy also assured Montevideo stayed in Brazilian hands). Could Brazil do so? Maybe, maybe not. Both sides were exhausted by early 1828, that's why they accepted mediation to end the war.