I’ll Have Another overhauled a tiring Bodemeister to win by 1 ½ lengths. He paid $32.60, $13.80, and $9. He ran 1 ¼ miles in 2 minutes 01.83 seconds.

Bodemeister, trained by three-time Derby winner Bob Baffert, was second and returned $6.20 and $5.60 as the 4-1 favorite. Dullahan was a neck back in third and paid $7.20 to show.

O’Neill didn’t waste any time vowing that I’ll Have Another will go on to the Preakness in two weeks.

“Maryland, here we come, baby!’’ he said.

I’ll Have Another made his way to the starting gate accompanied by his stable pony, Lava Man, another cheap purchase turned into a career winner of more than $5 million by O’Neill. The trainer has made his name predominantly in Southern California, although he has won three Breeders’ Cup races.

One of his best horses, Steviewonderboy, was the winter favorite for the 2006 Derby before being sidelined by injuries.

A hot pace was anticipated from speedster Trinniberg, although surprisingly it was Bodemeister under jockey Mike Smith who blazed to the front and forced Trinniberg to take a back seat. In the late-afternoon heat, Bodemeister set impossibly fast fractions. He ran the opening quarter-mile in 22.32 seconds and the half-mile in 45.39.

“I told Mike, ‘Look, if he breaks great and feels like running, we can win it,’ ’’ said Baffert, who was recovering from a heart attack in Dubai five weeks ago. “That’s the only time I’ve run second where I’ve been happy, because he ran his race.’’

Meanwhile, I’ll Have Another was comfortably galloping along behind the blazing speed. Gutierrez angled his colt clear on the final turn and took dead-aim at Bodemeister, who was clearly in front at the top of the stretch.

“I knew we were in trouble when I saw Doug’s horse coming,’’ said Smith, who won the Derby with 50-1 shot Giacomo in 2005.