Chesney Hughes batted throughout the opening day for a career-best 171 not out as Derbyshire piled up 302-4 after being sent in by Yorkshire at Headingley.
Opener Hughes and Wayne Madsen put on 258 for the second wicket in 68.1 overs after Tim Bresnan (1-58) had removed Billy Godleman (2) with the new ball when play got under way 45 minutes late due to a wet outfield.
Hughes was given a life on 70 when he edged Bresnan and wicketkeeper Jonathan Bairstow dropped the catch moving in front of first slip.
The Anguilla-born batsman went on to bring up his fifth first-class century from 160 balls, while his skipper Madsen was content to play a supporting role.
Madsen's departure for 93 to Steve Patterson (1-47) sparked a late rally from Yorkshire as they picked up three wickets for 34 runs.
Leg-spinner Adil Rashid (1-92) had Shivnarine Chanderpaul caught by Adam Lyth for four and Liam Plunkett (1-52) sent Wes Durston (3) on his way.
But Hughes remained unbeaten at the close having hit 25 fours and three sixes in his 282-ball stay.