Bryant scored 32 points, O'Neal added 27, and the Lakers got great support in a win that gave them a 3-2 lead in their Western Conference first-round playoff series.
The fifth-seeded Lakers appeared to be in trouble after losing Game Three at home in overtime to fall behind in the series, but they evened things with a win in Game Four on Sunday, and showed their huge advantage in experience Tuesday.
As usual, the three-time defending champions relied heavily on Bryant, who scored 16 points in the third quarter, and O'Neal, who made 10-of-18 shots and pulled down 11 rebounds.
"Experience pays off when you get in games like this," Bryant said. "We know how to handle it and know how to apply pressure to the other team. We don't need to get too excited about this win. We did what champions are supposed to do."
"We just had a little bit more intensity than they did," O'Neal said. "This is the first game in a long time we've had a good four quarters."
Fisher, who had been outplayed by Minnesota guard Troy Hudson, scored 24 points. Horry, who had not made a three-pointer in the first four games, made two in a second-quarter surge that gave the Lakers the lead for good.
"Tonight we set the tone early, and those first few minutes in the third period were extremely important," Fisher said.
Playing their 600th playoff game in search of their 15th championship, the Lakers thoroughly outclassed the Timberwolves, who were playing their 28th playoff game in search of their first series win.
In what may have been the biggest game in the history of the franchise, Minnesota came up very small. Superstar Kevin Garnett had 25 points and 16 rebounds, but got very little help.
"It's win or die (now)," said Garnett. "We've got all the confidence in the world and we've won at Staples before. I hope they don't think it's over, because we're coming."
The Lakers can advance to the conference semifinals for the seventh straight year with a win at home Thursday.