Los Angeles evened the best-of-seven Western Conference first-round series at two games apiece.
The three-time defending champion Lakers appeared to be in major trouble with 1:57 left in the third quarter, when the Timberwolves took a 74-63 advantage on a three-pointer by Troy Hudson.
But Los Angeles scored the final eight points of the period and tied the game on a three-pointer by Bryant with 10:49 remaining.
"We knew that we needed this game and we play our best when our backs are against the wall," said O'Neal, who posted his eighth career playoff game with at least 30 points and 20 rebounds. That is one more than every other active player in the league combined.
The Timberwolves scored the next six points and held an 87-82 lead after Anthony Peeler went one of two from the line with 6:34 left. But the Lakers reeled off eight straight points, taking the lead for good at 88-87 on a jumper by Devean George with 4:40 to play.
After Kevin Garnett got Minnesota within 96-95 on a shot from the arc with 35 seconds left, Bryant missed a hanging jumper in the lane, but O'Neal tipped in the rebound to make it 98-95 with 19 seconds to play.
Garnett, who made his first seven free-throw attempts, was fouled four seconds later but missed both shots, and Bryant gave the Lakers a five-point lead with a pair from the stripe with 12 seconds left.
"It humbles you very quick," Garnett said. "The ball actually felt pretty good coming off my hand. I missed them. But I'll take them anytime."
Garnett made it 100-97 with a turnaround jumper with 8.8 seconds remaining, but Bryant iced the game with another pair from the line with 7.2 left.
Bryant shot just seven of 25 from the field, but went 16 of 17 from the line.
"I don't get too many wide-open jump shots," he said. "They just pretty much stay inside my shirt 'til they find out what kind of deodorant I have on."
O'Neal, who made half of his 26 shots, was only eight of 15 from the line but grabbed 10 offensive rebounds -- two more than the Timbwerwolves.
"I've got to get the damned ball," he said. "Bring the ball and throw it to me every time. If I get the ball every time, I can do what I do and we're fine."
"When it's a critical game, he always comes in with that look in his eyes," Lakers guard Brian Shaw said of O'Neal. "You always know he's going to perform like he did tonight."
Los Angeles outscored Minnesota on second-chance points, 29-2.
"It was a survival game," Lakers Coach Phil Jackson said. "Our bench gave us a big game. We had second-chance points that I thought were overwhelming. That's the difference in this ballgame, considering the urgency that we had to play with."
"We (allowed) 18 offensive rebounds for 29 points -- two things that are our strengths really were our weaknesses tonight," Minnesota Coach Flip Saunders said. "But they did a good job. Shaq was extremely aggressive tonight, he had by far the best game of the whole series. Their bench came in and they played extremely well for them in the second half."
The Lakers lost forward Rick Fox to a strained left ankle tendon with 6:37 left in the first quarter. He did not return and will have an MRI taken Monday.
Garnett and Hudson each scored 28 points and Garnett added 18 rebounds for Minnesota, which held Los Angeles to 40 percent shooting but connected on just 43 percent.
The Timberwolves scored the final nine points of the first quarter to take a 26-25 lead and held a 45-43 edge at the break behind 20 points from Hudson and 10 points and 11 rebounds from Garnett.
O'Neal totaled 21 points and 11 rebounds in the half.
"Rick went out and we realized early in the first half that he was not going to return," Jackson said. "Devean got into foul trouble and Kobe moved to small forward. But we were able to survive it, even though we weren't very efficient or very fluid as a basketball team during that period of time."
Game 5 will be Tuesday night in Minneapolis.
"Our guys in the locker room are not satisfied, even though we came in here and got one and one and had opportunities down the stretch," Saunders said. "Let's tip it up again on Tuesday."
"It's like there's a heavyweight championship belt and we're trying to take it away," Garnett added. "We're confident. We had them on the ropes and they know it."