Joe Simmonds' penalty three minutes from time sent Exeter through to the Anglo-Welsh Cup final after a 20-17 win over Newcastle.
The Chiefs trailed 17-7 at the interval but a strong second-half performance booked a date in next Sunday's final at Kingsholm against Bath.
It will be Exeter's fourth consecutive appearance in the final and they will be hoping to go one better next week after narrowly losing the last two.
Simmonds and Stu Townsend scored tries for Exeter, with Simmonds converting both and adding two penalties.
Simon Hammersley and Kyle Cooper went over for the Falcons and Toby Flood added two conversions and a penalty.
Exeter took the lead with a splendid try in the third minute. Argentina international Santiago Cordero fielded a clearance before sailing through a huge gap in the visitors' defence with Townsend up in support to receive the scoring pass.
Minutes later, Chiefs looked set for a second try when Ollie Devoto brushed aside more weak tackling from Newcastle but the centre was foiled by the Falcons' last line of defence in full-back Hammersley.
Flood got his side on the scoreboard with a penalty before they suffered a setback when prop Sam Lockwood left the field with a nasty cut to his head.
The wind made conditions difficult as both sides struggled to bring any continuity to their play and it took a driving line-out to record the next score when Cooper crashed over to give Newcastle the lead.
Lockwood returned with his head heavily bandaged but the errors continued with visitors' centre Josh Matavesi twice kicking the ball straight out of play but despite that, his side went further ahead.
Number eight Nili Latu burst away from a maul on halfway to run 35 metres before the ball was recycled for Ally Hogg to send Hammersley over and give Newcastle a 17-7 half-time lead.
Exeter had the advantage of the wind in the second half and soon benefitted when after a period of sustained forward pressure, Simmonds side-stepped past Hammersley to score.
Chiefs continued to dominate the third quarter but could not turn their possession and territory into points and still trailed 17-14 going into the final 20 minutes.
A lengthy touch-finder from Devoto secured Exeter a platform in the opposition 22 and when the visitors were penalised at a scrum, Simmonds brought the scores level before Flood was short with a penalty attempt from long distance.
Simmonds then held his nerve to land the match-winner before replacement Joel Hodgson had a chance to take the match into extra-time but his kick, the last of the match, fell narrowly short.