Trainer Aidan O'Brien claimed a sixth Chester Vase win as Hans Holbein scored under a front-running Ryan Moore ride.
The 7-4 favourite stayed on well to see off Storm The Stars by one-and-three-quarter lengths.
Hans Holbein, named after a 16th century portrait artist, was cut to as low as 16-1 (from 66-1) by bookmakers for next month's Derby at Epsom.
"He went round here well enough so I don't see why he wouldn't act at Epsom," said Moore.
"He's quite laid-back but he finds a little bit when you ask him."