Sussex all-rounder Wiese's hit the first championship century of the season, a cleanly-hit 106 (105 balls, 14 fours, three sixes), as his side replied to 299 with 374 all out.
He eventually fell to Stone, the seventh of eight victims for the former Northamptonshire fast-bowler, who ended with a career-best 22.5-4-80-8 on his home championship debut for Warwickshire.
Sussex captain Ben Brown will also take plenty from the game. His first innings as club captain brought an assured 91 (174 balls, eight fours) against a Warwickshire attack which, Stone apart, looked understandably rusty having not had a single full day in the field in their pre-season schedule due to rain.
For the game as a contest, however, there was no way out of the cul-de-sac up which it was forced by the loss of 150 overs, including the entire first day, to the weather. Warwickshire closed on 87 for three in their second innings.
After Sussex resumed on the final morning on 194 for six, Ollie Robinson soon edged Keith Barker behind but Brown and Wiese helped themselves to important early-season time at the crease in a partnership of 155 in 30 overs. Wiese batted forcefully from the off, hitting cleanly on his way to three figures in 91 balls - his century before lunch all the more creditable when compared to the batting travails of most counties in the opening round of matches around the country.
Stone, having taken the first six wickets on the third day, then returned to add the last two, trapping Wiese in front and bowling Ishant Sharma who, having just top-edged a six, attacked again and this time missed.
Sharma, making his Sussex debut, then seized the chance to stretch his legs in the last session of the match. After Robinson knocked out Will Rhodes' off-stump, Sharma charged in from the Pavilion End during a pacy spell which brought him the wickets of Ian Bell, caught behind, and Jonathan Trott, lbw. Dominic Sibley stilled any Warwickshire nerves though with an steady unbeaten 42 (89 balls) to see the game out.
Sussex will hope for better weather and a full four days of action at Leicestershire, starting Friday.