Hampshire 102 for 5 (Prest 25, Weatherley 25) beat Worcestershire 100 (Usama Mir 39, Ellis 4-6) by five wickets
Ellis claimed 4 for 6, with Chris Wood and John Turner both picking up two scalps each in a supreme bowling performance.
The Rapids had an enterprising 70-run stand between Usama Mir and Ed Pollock - but it was bookended by slumping to 29 for 6 and then losing the last four wickets for one run as they were rolled for 100.
The Hawks spluttered to the target to win by five wickets and reach their 10th Finals Day and maintain their hopes of being the first team to win the Blast back-to-back.
The Rapids had never played a Blast match at the Ageas Bowl, and had only faced the Hawks once in the format. On that occasion, in 2015, James Vince blitzed an unbeaten century as Hampshire totted up 196 before Worcestershire reached 58 for 2, then the floodlight-less New Road got too dark.
The Rapids would have dreamed of a total eclipse of the hot evening sun and a power failure amid their first collapse, which began with a wicket in each of the first four overs.
Jack Haynes lasted until the fourth ball of the innings before a leading edge was well caught and bowled by Chris Wood.
The Blast's breakthrough fast bowler John Turner added Brett D'Oliveira as his 19th victim by cartwheeling his leg stump after an attempted scoop.
Mitchell Santner and Adam Hose both picked out fielders - a brilliant long on catch from Vince and spliced to square leg respectively.
Two wicketless overs were a mere interlude before James Fuller's wicket maiden accounted for Kashif Ali and Ben Cox chipped to midwicket.
But Mir and Pollock salvaged things with a 70-run stand, which included 16 runs off a Liam Dawson over, with the fifty-partnership coming off 45 balls with a six over long on.
The second collapse was as ugly as the first as four wickets fell in eight balls for a single run to end a sorry innings.
Mir's thick outside edge off Benny Howell was easily caught at short third before Ellis splayed the tail with three wickets in four balls - Adam Finch yorked, Dillon Pennington caught at cover and Pat Brown leg before.
Aneurin Donald replaced Ben McDermott - who had a back spasm - with the gloves and at the top of the order, and crunched the first ball of the reply through the leg side but edged behind soon after.
Vince was caught at cover but is now 20 runs away from equalling his 678 runs from last season - reaching that would give him the best three Blast seasons. It is not beyond the realms of possibility that he could better his annus mirabilis of 710 runs in 2015.
Tom Prest hit three fours and a six in a happy-go-lucky 25 before he was well caught playing the reverse sweep, with Dawson falling in similar style.
Joe Weatherley got the run chase within five before skying but the Hawks stayed on track for a third Blast title and condemned the Rapids to their sixth quarter-final defeat in eight attempts.