With $270,000 at stake in the sudden-death play-off of the Walt Disney World-Oldsmobile Classic and a huge gallery holding its breath, David Duval lined up his putt, tapped the ball calmly and watched it roll 15 feet into the hole. Instantly the crowd exploded in cheering. But the man of the hour barely cracked a smile as he plucked his ball from the cup and strolled off the green. "In all the years I've been watching golf, it was one of the most shocking things I've seen," says NBC golf analyst and former U.S. Open champ Johnny Miller of Duval's performance that afternoon in October 1997. "That was a big putt, and he acted like it was a practice round. But when David goes on a golf course, he goes to war."

Lately Duval, 27, has been mounting one of the most successful campaigns since the days when Arnie's Army was in full force. His take-no-prisoners attitude and precise ball striking have brought him nine PGA tournament victories in the past 18 months, the kind of streak rarely seen in a sport known for its parity. Duval also earned a place in golf legend this January at the Bob Hope Chrysler Classic by shooting a final-round 59, a score achieved only twice before in the 83-year history of the PGA. "When you think about how many rounds of golf have been played and there's only been three of them," says Duval, "you have a better chance of getting attacked by a shark or struck by lightning."

Chances are his reaction would be similarly muted under either circumstance. So if Duval wins next week's Masters tournament in Augusta, Ga., don't expect to see him high-fiving it with the gallery. "He really does have a big heart—he just doesn't show it very often," says Duval's girlfriend of four years, Julie McArthur, 32. "The hard part is getting him to let you into his world."

It's no accident that Duval, whose masklike wraparound shades are his tour trademark, prefers to hide his emotions. Growing up in Jacksonville, Fla., the second of three children of Bob Duval, then the pro at the Timuquana Country Club, and Diane, a secretary, he experienced enough pain to last a lifetime.

In December 1980, when David was 9, doctors diagnosed his 12-year-old brother Brent with the rare blood disease aplastic anemia. His only chance for survival was a bone-marrow transplant—with David as donor. But first, David had to undergo an excruciating preliminary procedure to assess his marrow. With only a light anesthetic to numb the penetration point, a doctor stuck a thick needle into his lower back, through the muscle and into the bone. "I'll never forget it," Duval says. "I was laying on the table yelling and screaming."

But the worst was yet to come. Although the subsequent transplant appeared to be a success, Brent's condition had deteriorated rapidly by April. After a couple of weeks in a coma he died—of graft-vs.-host disease. When David's transplanted bone marrow started to take, his immune cells began attacking Brent's body. "David took it really hard," says his father. "He thought he killed his brother because it didn't work. He became very serious after that, very focused and disciplined."

Over the next few years, David poured himself into golf. The sport "lends itself to solitude," observes Duval. "You can practice some and play a round, and it takes up a big chunk of a day. It's all-consuming."

After attending Georgia Tech, where he made first-team All-America all four years, Duval turned pro in 1993. Before beginning his winning streak in October 1997, Duval was a frustrated tour bridesmaid, finishing second seven times in 92 events. Observes Miller: "He couldn't quite figure out how to win, but once he did, it was 'See you later.' "

Though Duval earned a record $2.6 million in purses last year, he is hardly the type to flaunt it. Describing himself as "a jeans-and-T-shirt kind of guy," he shares a three-bedroom home near the beach with McArthur, a former pharmacist, not far from where he grew up. (Divorced in 1996, Duval's father is now a successful player on the PGA Senior Tour, while his mother just moved into a new house that David bought for her.) Although he is as private in his way on the course as he is off, his galleries these days are starting to rival even those of Tiger Woods—whose reputation as Best in the World he has challenged—and Duval doesn't seem to mind it a bit. "When people stop asking for autographs," Duval says simply, "I won't be playing too good."