Exeter scored with two minutes left on the clock to reach a second successive Premier 15s final, ending Saracens' perfect semi-finals record.
Sarries led 14-0 at the break, but the Chiefs went ahead in the second half as the visitors went down to 13 players.
Back to 15, Saracens piled on pressure and Jess Breach gave them the lead.
Another yellow card gave Exeter a numerical advantage again and Eilidh Sinclair crossed to seal victory in front of a jubilant Sandy Park.
The Chiefs will play Gloucester-Hartpury in the final at Kingsholm on 24 June.
Exeter exact revenge for 2022 final
Three-time champions Saracens had reached all four of the previous Premier 15s finals, and beat Exeter to claim the title in last year's edition.
They had never won at Sandy Park, though, and initially looked set to change that as England prop Hannah Botterman broke through a defiant Exeter defence to score, before Sarah McKenna went over shortly after.
Exeter responded exactly as they needed to after the break. Katie Buchanan made a sensational break, tearing down the field before Kate Zackary crossed just 45 seconds after kick-off.
Liv McGoverne cut Saracens' lead to 14-10 with a penalty, before the visitors earned two yellow cards within a minute of each other - both Holly Aitchison and co-captain Marlie Packer going to the sin-bin for deliberate knock-ons.
Exeter took their opportunity, building through phases before Hope Rogers crossed from short range and McGoverne landed the conversion to give them the lead for the first time at 17-14.
Still Saracens could not be stopped. They inched towards the tryline and, with Exeter's defence holding firm, Aitchison opted for a cross-field kick that allowed her England team-mate Breach to score.
Exeter soon applied pressure at the other end. Eventually Saracens' Georgia Evans was shown a yellow card in the 78th minute and Sinclair took her chance to seal victory.
"The girls were unbelievable," Exeter head coach Susie Appleby said.
"The biggest thing about our players is they never say die. They think they can do things from anywhere, which I absolutely admire.
"I love them. They're absolutely amazing. We get to stay together for another two weeks, which is so exciting."
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