Wednesday's result was Brazil's fifth win in five games and meant they will face either Spain or Italy in Sunday's final at the Maracana in Rio de Janeiro. The European duo meet in Fortaleza on Thursday.
Both sides said the decisive moment of the match came in the 13th minute when Chelsea defender David Luiz wrestled Uruguay captain Diego Lugano to the ground. Diego Forlan's weak penalty was well saved by Julio Cesar, who dived to his left to turn it round the post.
"More than having an effect on my team, it had a huge effect on the opponent," Uruguay manager Oscar Tabarez told a news conference.
"They had been second best until then and as of that moment they grew."
But it took Uruguay just three minutes of the second half to draw level. The Brazilian defence repeatedly failed to clear the ball and when Thiago Silva's weak pass fell to Cavani he made no mistake with an angled drive.
Uruguay's front three of Forlan, Luis Suarez and Cavani failed to get the better of Brazil's back-line and Neymar was a shadow of the player who won the man of the match award in his last three games.
Nevertheless the win was Brazil's fourth in four games at this year's tournament and their fifth in a row under Luiz Felipe Scolari, a run that belies their 22nd place in the FIFA rankings, their lowest ever.
"If you keep plugging away something good will happen and that happened today," he said.
"Four wins in four games is important," he added. "We are on the right track."
