Magnus Larsson upset Swedish Davis Cup teammate Stefan Edberg 6-4, 6-7 (7-9), 8-6, while Todd Martin beat Karel Novacek 7-6 (7-5), 6-4, also reaching the last eight.
Sergi Bruguera completed the quarterfinal lineup with a 5-7, 6-4, 6-0 victory over Andrei Medvedev, who was treated for a foot injury in the third set.
In first round action yesterday, Pete Sampras advanced over Jaime Yzaga, of Peru, 6-2, 6-4. Becker won a tight match against Wayne Ferreira of South Africa, 5-7, 6-4, 6-3, Michael Chang defeated Alberto Berasategui of Spain, 6-1, 7-5 and Goran Ivanisevic ousted Jonas Bjorkman of Sweden.
In the quarterfinals, Larsson will face Agassi and Bruguera will play Martin.
The $6 million Compaq tournament invites 16 players with the best records in the four Grand Slams -- the Australian, U.S. and French Opens and Wimbledon
Agassi wore down Muster in a duel of powerful baseline hitters.
"I have a bit of a cold, I didn't feel like I was 100 percent," Agassi said.
Muster said Agassi had become "world class" on all surfaces.
"He is definitely in great shape right now, he's hitting the ball extremely well," Muster said.
After trading early breaks, Agassi broke again for a 5-3 lead. Muster saved one break point after one of the most spectacular rallies.
Chasing a Muster lob, Agassi returned the shot through his legs, but Muster had come up to the net and scored with a volley. Agassi liked the rally so much that he stood and watched the replay on the scoreboard television screen.
The second set went with serve until the 11th game, when Agassi broke for a 6-5 lead.
Agassi won the applause of the 11,000 fans in the Olympic Hall in the previous game. On the opening point, one of Muster's shots hit the line, but the umpire called it out.
The fans went into an uproar and only allowed the match to resume when Agassi conceded the point.
"I knew it was on the line before it bounced," Agassi said. "The crowd was going nuts and I couldn't say anything until they calmed down."
"My serve was very weak and that cost me the match," Muster said.
Larsson and Edberg led Sweden to victory over Russia for the Davis Cup title last weekend in Moscow, but they battled hard for two hours and 18 minutes Wednesday.
Larsson wasted a match point before losing the second set tiebreak, but he rallied to win the third set, converting his third match point with a forehand passing shot off Edberg's serve.
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