Resuming on 142-9 after a rain-hit day one, Derbyshire added just eight runs as Ben Cotton fell to Steve Magoffin.
Sussex's openers made a 113 partnership before Chris Nash (65) was bowled by Wayne Madsen (2-65), but Joyce (106), Wells (104 not out) and Ross Taylor (54) helped the hosts build a big lead.
Matt Machan was out to the final ball of the day as Sussex closed on 342-4.
Sussex built a commanding first-innings lead over Derbyshire on day two at Hove as Ed Joyce and Luke Wells made tons.