Brazil outplayed Costa Rica for 90 minutes, but managed only a goal by Muller in the first half for a 1-0 victory in Turin, Italy.
Brazil has four points from its opening two games in the 24-nation tournament to assure a spot in the second round. The three-time champion joined Cameroon, Italy, Czechoslovakia and West Germany.
The heavily favored Brazilians had no trouble with the Costa Rican defense. But goalkeeper Luis Conejo, a star in his team's 1-0 win over Scotland, was just as good this time.
Muller scored in the 33rd minute when his hooked shot flew past Conejo after it deflected off defender Mauricio Montero. Conejo made nearly a dozen difficult saves.
Costa Rica, still in the running for the second round, will play Sweden Wednesday.
The Brazilians dominated in the first half, restricting Costa Rica to an occasional breakout.
Midfielder Alemao set the pattern in the first minute, firing a shot just inches wide. In the second minute, Careca and defender Roger Gomes rose high together and the ball flew off the crossbar.
Brazilians Jorginho and Mozer were cautioned for the second time in the tournament and will miss the team's final first-round match, against Scotland. A tie in that game Wednesday would give Brazil the Group C title.
Scotland 2, Sweden 1: In Genoa, Italy, Scotland made wholesale changes and used them well to keep alive its hopes of reaching the second round of the World Cup for the first time.
Midfielder Stuart McCall scored from close range in the 11th minute. Striker Mo Johnston converted a penalty kick to put the game away with eight minutes to play.
Substitute Glenn Stroemberg scored for Sweden with four minutes left. The Swedes, who lost by 2-1 to Brazil in their opener, pressed for the tying goal and had two good chances. But goalie Jim Leighton held them off.
McCall's goal followed a corner kick by Murdo MacLeod that found David McPherson, who headed it toward McCall. He beat the defense to score.
Scotland juggled the lineup, pairing McPherson and Craig Levein and using Robert Fleck on the attack.