Exeter stunned Bath in a dramatic second-half fightback to deny the hosts a third successive Gallagher Prem final appearance.
The Chiefs’ thrilling 27-26 win, in which they wiped out a 16-point interval deficit to score 17 unanswered second-half points, ended Bath’s hopes of joining an elite group of clubs to win back-to-back titles.
The Chiefs will play Northampton at Allianz Stadium next Saturday.
Only three clubs – Wasps, Leicester and Saracens – have won Prem silverware in successive seasons since play-offs were introduced 24 years ago, and membership of that group agonisingly eluded Bath.
The home side went through 40 phases of play during a frantic finale, but replacement prop Billy Sela was held up over the line, and Chiefs had made it mission accomplished.
Bath dominated the first half, scoring tries through Beno Obano, Thomas du Toit, Joe Cokanasiga and Henry Arundell, while Santi Carreras kicked three conversions.
But Exeter somehow turned things around following touchdowns from Christ Tshiunza, Ben Hammersley, Greg Fisilau and Ethan Burger’s 68th-minute clincher, with Henry Slade kicking two conversions and Harvey Skinner landing a penalty.
Exeter made a lively start and breached Bath’s defence inside three minutes, but wing Campbell Ridl’s touchdown was rightly ruled out following Slade’s forward pass.
Bath were soon into their familiar stride, though, and after Slade was yellow-carded by referee Christophe Ridley after illegally halting an attacking phase, Obano crossed from close range and Carreras converted.
With Slade temporarily out of the action, Skinner assumed kicking duties and landed a 15th-minute penalty to cut Exeter’s early deficit.
But Bath were soon back on the front foot, making their numerical advantage count through a second try, this time following number eight Alfie Barbeary’s half-break and Du Toit powering his way over. Carreras’ conversion made it 14-3.
It was a sizeable advantage for Bath, yet Exeter stung them through a superb solo try from Tshiunza – complete with celebration swallow-dive – that Slade converted to give Chiefs’ travelling fans plenty of encouragement.
But Bath had momentum, and Cokanasiga scored their third try that was created by centre Ollie Lawrence, before Carreras added another conversion.
Cokanasiga’s brute strength had caused Chiefs sufficient trouble for rugby director Rob Baxter to make a 31st-minute substitution, sending on Hammersley for Ridl and switching Olly Woodburn from full-back to wing.
There was no let-up from Bath, and Arundell’s brilliant finish in limited space following a Ben Spencer cross-kick meant that Exeter trailed 26-10 at the break.
Exeter had the best of a tight third quarter, and they reduced their arrears in fine fashion when Woodburn and Slade combined slickly and Hammersley scampered his way across for a try that Slade converted.
And there was more trouble for Bath just before the hour when Chiefs struck again, this time through the rampaging Fisilau, and Exeter were suddenly just four points behind.
Chiefs’ cause was then helped by Cokanasiga receiving a yellow card for a deliberate knock-on, and Bath were under ferocious pressure as their healthy half-time lead looked in danger of evaporating.
Exeter then went ahead 12 minutes from time through Burger’s score, and the Chiefs showed admirable composure to close out a famous victory after Bath camped on their line during the closing seconds.
