Kentucky Derby winner Always Dreaming and Classic Empire, who started from gates four and five, broke out cleanly and ran alongside one another in a front-running duel through most of the mile and 3/16th race.
Classic Empire, who was fourth in the Derby after a bumpy start over the sloppy Churchill Downs track, looked primed to make amends when he pulled away midway around the final turn.
But Cloud Computing poured it on down the stretch with a charge from the outside to finish in 1:55.98 and clinch his second career victory.
Always Dreaming, who had faded after the turn for home, finished eighth in the 10-horse field on a fast track at Pimlico Race Course.
Cloud Computing was competing in his first race since the Wood Memorial six weeks ago. The horses who competed at the Derby had just a two-week layoff.
"I'm not going to dispute the fact that I brought in a fresh horse as part of our strategy," trainer Chad Brown said after his dark brown colt gave him his first Triple Crown victory.
"Classic Empire and Always Dreaming are two outstanding horses, and our strategy was if we are ever going to beat them let's take them on two weeks' rest when we have six (weeks), and it worked."
Winning jockey Javier Castellano, who won the Preakness in 2006 aboard Bernardini for his previous Triple Crown success, said the victory would be treasured by his entire racing family.
"My father was a jockey for 25 years, my uncle, my brother. We grew up in racing. It's really special for us," Castellano said.
"We been working for a long time for this moment. It's great for the family."
Cloud Computing paid $28.80, $8.60, $6.00 for a $2 bet, while Classic Empire paid $4.40, $4.00 and Senior Investment $10.20.
The final race of the series for three year olds will be the Belmont in Elmont, New York, on June 10.
(Reporting by Larry Fine in New York, editing by Gene Cherry/Greg Stutchbury)
