Lyth went to 50 for the eighth time this season in the heart of the afternoon session, off 117 balls.
An impressively watchful effort on a pitch with some juice in it, which has not been easy to score runs on, Lyth and Wharton quietly put their county into a very strong position.
Wharton claimed a stunning outfield catch at deep square-leg on day one and with the bat, he was more aggressive than Lyth, highlighted by successive sixes off Carson to move into the forties and take his side to 161-2.
The first was pulled, the second lofted handsomely over long-on.
Wharton reached his seventh fifty of the season shortly afterwards, off 79 balls, and by this stage him and Lyth were upping the ante.
Lyth reached the 1,000 mark just before tea where Yorkshire got to in rude health at 199-2 from 58 overs, the third successive season he has achieved the feat.
His third Championship century of the summer came up in 200 balls just after tea, with Yorkshire taking the lead moments later.
Sussex’s attack, missing Jofra Archer because of England and Ollie Robinson through injury, came under increasing pressure.
But they hit back midway through the evening session to get rid of Lyth and Wharton inside three overs, leaving Yorkshire 250-4 in the 74th.
Lyth was stumped by John Simpson off Carson – two for 70 from 28 overs – and Wharton bowled by the left-arm spin of James Coles.
Matthew Revis and Harry Duke then saw the day out for Yorkshire with 22 and 20 respectively.
