Midfielder Mineiro latched on to a clever through-ball from Aloisio to beat goalkeeper Pepe Reina in the 27th minute and give the South American champions their third world title.
Mineiro's strike snapped Liverpool's club record of 11 successive clean sheets and was the first goal the European champions had conceded in 1,042 minutes.
Liverpool almost struck back moments later 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 fired 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 while Morientes's spectacular overhead kick flashed just wide as Liverpool, cheered on by a majority of the 68,000 crowd, probed for an equaliser.
The referee also ruled out a Sami Hyypia effort, adjudging that Alonso's corner had curled out before the big Finn got on the end of it, while substitute Florent Sinama Pongolle's late effort was disallowed for offside.
Sao Paulo won the World Club Cup -- the tournament's forerunner, involving the champions of Europe and South America -- in 1992 and 1993.
