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.

Seven were taken to hospital, two in a serious condition, after the fire at Standon House Care Home in Tamworth, Staffordshire, on Saturday night.
The fire was accidental, caused by "poorly discarded smoking materials," Staffordshire Fire and Rescue Service said.
All residents were moved to alternative accommodation, police said.
About 20 firefighters were sent to the property, which suffered "very considerable" damage, the ambulance service said.
The ambulance service said 16 residents were rehoused within adjacent flats, with a further two people taken by ambulance to other care homes.
Emergency services were called to the home in Ashby Road at 23:00 BST and "fortunately, firefighters and staff were able to bring all of the residents out of the building," the ambulance service said.
Six people, including the two in a serious condition, were taken to Good Hope Hospital in Sutton Coldfield with a further patient taken to Queen's Hospital in Burton.
The seven were taken to the hospitals to be "assessed after smoke inhalation," Staffordshire Police said.
Insp Beverley Rounds, of Staffordshire Police, said: "We've had a number of calls from people living nearby and we want to thank them for their vigilance and reassure them the residents have been evacuated."

30 November 2015 Last updated at 16:35 GMT
Simon Whittaker, originally from Cheadle, posted his footage on Facebook saying: "Monarch A320 drifts off the centre line in cross winds at manchester airport and goes around."
Mr Whittaker, who used to fly planes himself, was on his way for a coffee at the Airport Hotel Pub when he noticed how the wind was affecting the incoming flights and began filming.
He said the weather was "absolutely treacherous" but that the pilot seemed "in control of the plane throughout the aborted landing". He said the winds were so strong that it was a challenge even keeping the camera steady.
Five planes were diverted from the airport on Sunday as a result of the high winds.
A spokeswoman said three planes were diverted to East Midlands Airport including two Monarch flights and another two went to Birmingham Airport.
The severe weather caused a roof on shops to be blown off in Greater Manchester, thousands of homes were left without power and trees were brought down.
Sussex built a commanding first-innings lead over Derbyshire on day two at Hove as Ed Joyce and Luke Wells made tons.
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At least 25 residents were evacuated from a care home after a large fire tore through the property.
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A plane aborted its landing at Manchester Airport after winds of up to 70mph swept across the North West.