Ridden by Martin Garcia, Drill ran seven furlongs in 1:21.28 and paid $9.60 and $5 at 7-2 odds.
Drill trailed pacesetter American Act most of the way until taking a small lead with a furlong to go and barely holding off his rival under Garcia's urging.
Drill is nominated to the Triple Crown series, but Baffert said he doesn't think the colt wants to run the Kentucky Derby distance of 1 1-4 miles.
"I wouldn't run out and buy a future book (bet) on him," said the Hall of Fame trainer, who is loaded with other Derby candidates. "He'd have to prove something to me going long. He's one-turn right now. In time he might be able to do it because he's learned to relax."
Drill's co-owner, Mike Pegram, agreed.
"This is a Breeders' Cup horse," he said. "I don't know which Breeders' Cup race. We'll just let him sort himself out."
Drill was trying to turn things around after not visiting the winner's circle since Sept. 7, when he won the Del Mar Futurity against Creative Cause. He was fifth in the San Pedro Stakes at Santa Anita on Jan. 22.
Pegram said three of Drill's previous losses were "throwout" races, but he had no excuse for a ninth-place finish in the CashCall Futurity on Dec. 11.
"He came out of those races really well. He always shows so much energy, he's taken a lot and he's handled it," Baffert said. "But today I could tell he was more relaxed in the race and he got an easy trip. That helps, too."
Creative Cause was fourth in the early going before getting up for third in his first start since finishing third in the Breeders' Cup Juvenile in November. He now has $506,000 in graded stakes earnings, all but assuring him a starting spot in the Kentucky Derby, which uses such earnings to determine its full 20-horse field.
"We got what we wanted out of the race. He's a route horse, not a seven-furlong horse," trainer Mike Harrington said. "We hope he moves forward off this. Did you see him gallop out? He'll definitely move forward."
Harrington has another Kentucky Derby candidate in Empire Maker, who finished second in the 1 1/16 miles Robert Lewis Stakes (Grade II) earlier this month at Santa Anita. The trainer, like Baffert, is carefully juggling his colts' schedules so they don't run against each other. Harrington said his next target will be the $300,000 San Felipe Stakes at Santa Anita on March 10 for one of them.
"I don't know which one," he said.
Whichever of Harrington's horses doesn't run in the San Felipe is possible for the $500,000 Rebel Stakes at Oaklawn Park on March 17.
Baffert is considering the San Felipe for Fed Biz or Liaison, two more of his top Kentucky Derby candidates. Another hopeful, BC Juvenile Sprint winner Secret Circle, is at Oaklawn awaiting a start in Monday's $250,000 Southwest Stakes.
First post time for a nine-race card on Monday is 12:30 p.m. The Grade II, $150,000 Buena Vista Handicap for older fillies and mares at one mile on turf is the afternoon’s feature.