The visitors trailed 17-3 at one stage but a much-improved second-half performance saw them run out deserved winners with a try from Harry Williams five minutes from time proving decisive.
Perry Humphreys scored two tries for Worcester, while Duncan Weir kicked two penalties and two conversions.
A Simmonds penalty gave Exeter an early lead before Worcester responded by scoring a superb try.
From a line-out, 40 metres out, Cornell Du Preez made the first dent in the Chiefs defence before he and Michael Heaney combined cleverly to find Humphreys, who evaded Stuart Hogg’s tackle to race away and score.
Weir converted before another barnstorming run from Du Preez won Warriors another penalty, which Weir knocked over from close to half-way to give the hosts a 10-3 lead at the end of an evenly contested first quarter.
Exeter then showed excellent ball retention and handling skills to create an opening for Alex Cuthbert, who burst into the opposition 22 only to then concede a penalty for not releasing when he was hauled down.
However, against the run of play, Warriors scored a second try. Flanker Sam Lewis burst away from a line-out in his own 22 before another surge from him took the hosts into Exeter’s half. From there, swift passing gave Humphreys the chance to outflank the cover and score his second.
Soon afterwards, Worcester suffered a setback when the impressive Lewis was led off after being on the receiving end when he attempted a tackle and his presence in defence was missed as Chiefs scored their first try.
A well-timed pass from Tom O’Flaherty sent Jacques Vermeulen haring through a gap and Maunder was up in support to score to leave Exeter trailing 17-10 at the break.
Lewis did not return for the restart with Marco Mama being a permanent replacement. Exeter also made a change, an optional one, with scrum half Nic White returning after his World Cup duties with Australia.
The visitors started dominating possession and territory and when Warriors replacement Michael Fatialofa conceded a needless penalty for a reckless challenge, they took advantage with Kvesic driving over from close range.
Simmonds converted but a second penalty from Weir put Worcester back in front with 11 minutes remaining but Williams rewarded a period of 32 phases by crashing over to complete the comeback.
Photos from the match
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