Midfielder Mineiro latched on to a clever ball from Aloisio to fire past goalkeeper Pepe Reina in the 27th minute, giving the South American champions their third world title.
Liverpool dominated for large periods, had three goals disallowed and a late penalty appeal dismissed as they failed in their bid to become world champions for the first time.
"We knew one of the goals was a clear goal," said Liverpool manager Rafael Benitez. "I was disappointed how the situation was controlled by the referee.
"I try to have a lot of respect but we deserved to win. We had 21 shots, 17 corners, we hit the crossbar twice and had three goals disallowed. We controlled most of the game."
Mineiro's strike snapped Liverpool's club record of 11 successive clean sheets and was the first goal they had conceded in 1,042 minutes of play.
"It was my only chance and it was like winning the lottery," said Sao Paulo's hero. "I managed to keep calm and put it away without getting nervous."
Liverpool almost struck back moments after the goal when Luis Garcia flicked a Xabi Alonso corner onto the crossbar.
Rafael Benitez's side should have been in front as early as the second minute when Spanish striker Fernando Morientes missed the target with a point-blank header.
Garcia came close with two more headers and Gerrard blasted wide in the 35th minute after good work from Harry Kewell on the left.
Gerrard forced a superb save from Sao Paulo goalkeeper Rogerio Ceni with a curling free kick six minutes into the second half.
Garcia had a headed goal disallowed for offside and Morientes's spectacular overhead kick flashed just wide as Liverpool probed for an equaliser.
Mexican referee Benito Archundia also ruled out a Sami Hyypia effort after adjudging that Alonso's corner had curled out before the big Finn volleyed it home.
Substitute Florent Sinama Pongolle's late effort was then disallowed for offside, to the annoyance of Liverpool's players and most of the 68,000 crowd.
Sao Paulo won the World Club Cup -- the tournament's forerunner, involving the champions of Europe and South America -- in 1992 and 1993.
"We beat a great team," said Sao Paulo coach Paulo Autuori. "The only thing that's important in football is the final score. Football is about having a winner and a loser.
"If you lose you always try to make excuses."