A 71st-minute red card shown to the Saracens lock Harry Wilson for a shoulder to the head of Rus Tuima, however, effectively sealed Sarries’ fate with Dan Frost registering a fifth Chiefs try.
Saracens needed something to get them going and finally found it after 27 minutes when the rapid Elliott somersaulted over in the right corner to give his side an 8-5 half-time lead.
Sarries had also travelled down without 16 first-team players either injured or away on international duty and the selection of the Welsh centre Nick Tompkins as a replacement back-row forward underlined the lack of available alternatives.
The Premiership is about to go into hibernation for two months and Exeter badly needed a mood-enhancing win before the Six Nations pushes the club game into the background.
It definitely did not help them, then, when their Argentina Juan Martín González flanker was sent to the sin-bin after seven minutes when Jacques Vermeulen was tipped out of a ruck upside down and landed on his head.
