Argentina international fly-half Ignacio Mieres slotted all of his five kicks at goal before being replaced when the Chiefs had built up a commanding 15-6 lead with the game going into the final quarter.
Worcester, who have not won away from Sixways in the Premiership victory since April 2009, replied through two Joe Carlisle penalties before his replacement Andy Goode earned them a third losing bonus point of the season, keeping them six clear of Newcastle Falcons.
The Chiefs gave a first-ever Premiership start to Wales international Craig Mitchell, at the expense of Hoani Tui, as one of three changes from the side that secured their second away win of the season at Sale Sharks last time out .
Fly-half Ignacio Mieres, who scored the winning try at Sale 40 seconds from time, started alongside scrum-half Haydn Thomas, replacing Gareth Steenson and Pat Phibbs respectively.
After a couple of minutes Worcester were penalised at a scrum on their own 22 and Mieres, with a slight breeze at his back, neatly slotted the ball between the uprights for the opening score.
But the Warriors were quickly back on level terms when Carlisle attempted a penalty from just inside his own half. The ball hit the crossbar, bounced up and down on to the bar again before finally going over.
Referee David Rose stopped the game on 14 minutes at a ruck and called the medical team on to attend to Warriors flanker Matt Kvesic, who was stretchered off with an injury to his left ankle before being taken to hospital.
The Chiefs then hammered away at the Warriors line with some good work from wing Gonzalo Camacho and centre Nic Sestaret, who linked up with their forwards before wing Marcel Garvey's thumping tackle halted the charge from lock James Hanks.
With 10 minutes of the half remaining Worcester were again penalised for failing to roll away after the tackle and Mieres' 30-metre kick from just to the left of the posts put the Chiefs back in front.
But minutes later the left boot of Carlisle, from out on the left, again levelled the scores after Exeter had been penalised for coming in at the side.
With less than three minutes of the half remaining the Warriors strayed offside and Mieres landed the simple 20-metre penalty. They then gave away a penalty at a scrum on halfway but Carlisle's kick went just under the bar, leaving the Chiefs with a 9-6 interval lead.
Exeter made a good start to the second half and their efforts were rewarded 12 minutes after the restart with a fourth penalty from the boot of Mieres, from in front of the posts, and then a fifth 10 minutes later before he was replaced for the final quarter.
Exeter were forced to defend for large periods in the final minutes of the game as the Warriors went in search of at least a losing bonus point, but the visitors were unable to break through.
With three minutes remaining the Warriors were awarded a 25-metre penalty, close to the right touchline, and ex-England fly-half Goode reduced the arrears to six points.
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