Hampshire 140 for 5 beat Essex 139 for 6 (Crane 3-18) by five wickets
Ian Holland held his nerve as Hampshire ended Essex's 13-month unbeaten run in all competitions.
All-rounder Holland snuck Hampshire over the line with a ball to spare to eke out a nervy five-wicket victory, having needed six off the final over.
Essex - who had been stunted by Mason Crane's impeccable 3 for 18 - hadn't tasted defeat since they lost to Somerset in the Vitality Blast on August 7 last year, although they are still winless as holders.
In reply to Essex's laboured 139 for 6, Hampshire rode their luck in the early stages. Scotland international George Munsey was dropped by Ryan ten Doeschate on 9, running back from point, and again on 12, this time by Tom Westley at mid-off.
His opening partner Tom Alsop was also given a life when Varun Chopra put down a one-handed reaction-effort at first slip.
Simon Harmer did make the breakthrough when Alsop - having struck the off-spinner for a four and six - was caught on the reverse by Westley, who appeared to dislocate his little finger in the process.
On a pitch being used for the third time, timing, and therefore scoring was difficult for both sides - with Hampshire reaching 64 for 1 at the halfway point.
Munsey, who top-scored with 32, attempted to boost the run-rate by top-edging Dan Lawrence over the ropes only to pick out deep fine leg two balls later off Aron Nijjar in the next over.
Left-arm spinner Nijjar, on his fifth T20 appearance, caused problems with his 2 for 25 - as Sam Northeast was brilliantly caught by Simon Harmer at short midwicket.
Lewis McManus was caught in the deep, but Joe Weatherley took Hampshire to within 14 runs of victory with a gutsy 27 but was bowled by a Paul Walter slower ball.
Having forced a tie against Surrey at the weekend, Matt Quinn was forced to defend six off the final over - which he failed to do on this occasion, as Holland and James Fuller rotated the strike nicely, before the former handed Hampshire their maiden victory in the 2020 Blast with a straight drive for the needed single.
Earlier, Sam Northeast had won the toss and stuck Essex in - with both sides naming unchanged XIs.
Cameron Delport survived carving straight to a juggling Fuller at point, but generally found himself shackled as Hampshire bowled accurately.
Teenager Scott Currie was struck for 16 in his sole over on debut, against Sussex, but found control and his maiden professional wicket - Chopra drilling to mid-on.
Crane, who had taken 3 for 24 at Chelmsford last season, continued the visitors' dominance through the middle overs.
The leg-spinner had Delport caught slog sweeping, Westley stumped and Dan Lawrence chipping a reverse sweep up to short fine leg Munsey.
But along with the regular wickets, Crane kept the run-rate down - only going for one boundary, a straight-six from Westley - as he returned 3 for 18.
The Eagles failed to hit a boundary between the ninth and 15th overs but thanks to the ageless ten Doeschate reached a competitive score.
The Dutchman enjoyed partnerships of 39 and 30 with Adam Wheater and Paul Walter, split by the wicket-keeper slapping Chris Wood to Northeast at extra cover.
Ten Doeschate, 40, showed little thrills with his unbeaten 37 from 29 ball, although did strike Wood back over his head for six.