Velazquez kept 9-2 shot Always Dreaming in a good position during the one-and-a-quarter-mile race and won by almost three lengths from Lookin At Lee.
Battle of Midway held on for third.
Pletcher said: "I thought we had a big shot when we turned for home. I was a little worried down the back side, but you could tell he was finishing."
Godolphin's Thunder Snow was slowly away and Saeed bin Suroor's charge was quickly pulled up by jockey Christophe Soumillon.
Always Dreaming gave trainer Todd Pletcher and jockey John Velazquez their second victories in the Kentucky Derby at Churchill Downs.