Clarke's unbeaten 110, coupled with a season's best 81 from a resurgent Jim Troughton, took the title contenders to a declaration at 400 for eight.
Yet even they must have been mildly surprised by the way Sussex collapsed for 191 in less than half a day with New Zealand off-spinner Jeetan Patel taking five for 77.
Six batsmen got into the 20s but no one did better than Luke Wright's 36 before he sliced Patel to deep point.
Clarke was again at the forefront for Warwickshire with three for 19 and Patel preyed on Sussex's vulnerability in an unchanged spell of 18.1 overs, which included the wicket of Matt Prior when the England wicketkeeper clipped to mid-on.
All this added up to a near-perfect day for the barnstorming home side. Five points for batting, three for bowling and three for a draw put them one ahead of overnight leaders Nottinghamshire with a game in hand.
For Sussex it was a no-win situation, although they did retrieve a couple of bowling points to keep their distance from the relegation strugglers.
Meanwhile in Division Two, Rob Newton and David Sales both scored centuries as Northamptonshire's batsmen dominated the second day of their match against Glamorgan at Wantage Road.
After the first day was washed out without a ball being bowled, Glamorgan won the toss and chose to field as the second day began on time.
Northamptonshire went on to close on 336 for five with Newton smashing a career-best 117 off only 113 balls - his sensational knock including 14 fours and three sixes.
Sales' innings was not quite as spectacular, but brilliant nonetheless as he made an unbeaten 129 off 277 deliveries with 16 fours.