A tentative start, which included just nine points being scored in the first half, was followed up by a frantic conclusion which saw the game won by Ben Spencer with the final kick of the game.
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First blood went Sarries' way when eventual match-winner Spencer kicked over a third-minute penalty, although Ceri Sweeney levelled things up soon after in the same manner.
It could have been even better for the Chiefs, though, who were only denied a try thanks to some solid goal-line defending from their opponents to hold up Elvis Taione.
Saracens, who find themselves one point and one place above Exeter in the Aviva Premiership table, were enjoying the lion's share of possession as the first half progressed, but the tie remained delicately poised.
Sweeney squandered a double chance to kick his side ahead when he hit the crossbar from a penalty, before following that up with another glaring miss.
Things turned in the holders' favour somewhat when Spencer was shown a yellow card having found himself on the wrong side of the ruck, with former Wales international Sweeney making no mistake this time to edge his side into a slender lead heading into the break.
Sarries really stepped things up following the restart, however, crossing over two times in the space of five minutes to race ahead.
David Strettle bagged both tries, the first of which came about after he intercepted Ben White's pass to coast in, while the second was more down to teamwork thanks to Spencer's successful crossfield kick into his path.
Strettle very nearly completed his hat-trick only for the ball to awkwardly bounce over his head when through, but it appeared to matter little when Nick de Jager powered over 18 minutes from time to put Mark McCall's men well in command.
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A dramatic late twist to the contest saw Max Bodilly pull his side right back into it, though, and when the full-back crossed over for a second time with just two minutes left to play Exeter gave themselves real hope.
Gareth Steenson successfully converted to take the scoreline to 20-20, although Saracens were awarded a penalty with time officially up to win the game, and Spencer made no mistake under pressure to ensure that there will be a new home for the cup this year.