Hampshire, set a victory target of 139 to secure runners-up spot and condemn the 2021 champions to the drop, were bowled out for 133 as Norwell, returning at the end of an injury-ravaged season, bowled magnificently in several spells from the Pavilion End to keep Warwickshire above the relegation trapdoor in the final moments of the season.
They resumed on the final day of the campaign on 62 for two but appeared to relinquish their survival hopes as they collapsed to 177 all out.
Dom Sibley, in his last game for the county before rejoining Surrey, made 77 from 101 balls but James Fuller (four for 34) and Brad Wheal (three for 68) exploited the hosts' desperate quest for quick runs.
Hampshire had 72 overs to reach their total but slumped to 91 for seven and, despite Nick Gubbins' steadfast 46, they fell just short to suffer an agonising defeat, as championship cricket delivered memorable entertainment.
With all the pressure on the home side, Hampshire set defensive fields in the morning and bowled well to them.
Wheal was first to benefit as Alex Davies (32) and Will Rhodes sent up catches, before Fuller capitalised when Dan Mousley and Jake Bethell perished on the ultra-offensive.
Sam Hain's runner was then run out by James Vince's direct hit, Danny Briggs clouted his first ball for six but found deep midwicket with another attempt, Fuller yorked Norwell and Sibley was last to go, lbw to Ian Holland, exiting to a fond reception.
Yorkshire-born Oliver Hannon-Dalby then struck first with a beauty which took Felix Organ's edge, before Norwell took over.
The 30-year-old bowled Holland, offering no shot, trapped Joe Weatherley lbw and had Vince caught at long leg. At 49 for four, it was very much game on.
Norwell returned just before tea to pin Ben Brown lbw and completed his five-for when Aneurin Donald chipped to extra cover. He then castled Keith Barker, before Gubbins and Fuller added 33 to take their side to the brink of victory.
However, the admirable Norwell had the final word, trapping Gubbins lbw, ripping out Fuller's middle stump and winning an lbw decision against Mohammed Abbas to seal a dramatic victory for the hosts.