Ignacio Mieres kicked all of Exeter's points as the Chiefs overcame Worcester in a close encounter at Sandy Park.
Mieres and Joe Carlisle exchanged two penalties apiece before the Argentine kicked a third to give Chiefs a 9-6 lead at the break.
The Exeter fly-half then added two more after the break to give the hosts a nine-point lead.
Carlisle's replacement Andy Goode then kicked a late consolation penalty to give Worcester a losing bonus point.
Exeter made three changes to the side that won at Sale last time out, with Wales international Craig Mitchell being given his first-ever start.
Worcester, who are six points clear of bottom-of-the-table Newcastle, have not won away in the Premiership since April 2009.
And, as well as suffering their sixth league defeat of the season, they also lost flanker Matt Kvesic to an ankle injury which saw him being taken to hospital.
Worcester head coach Richard Hill told BBC Hereford & Worcester:
"It could have gone either way and talking to their coaches afterwards they said there was nothing in it.
"There was literally one clear-cut scoring chance each in the game and both defences were firm.
"There was a huge amount of effort put in by both sides and unfortunately we have just come out on the wrong side."
Exeter: Arscott; Camacho, Sestaret, Shoemark, Jess; Mieres, Thomas; Sturgess, Clark, Mitchell; Hayes (capt), Hanks; Johnson, Scaysbrook, Baxter.
Replacements: Steenson for Mieres (63), Phibbs for Thomas (62), Tui for Mitchell (62), Phillips for Hanks (66).Not Used: Alcott, Moon, White, Tatupu.
Worcester: Classens; Garvey, Grove, Rasmussen (capt), Benjamin; Carlisle, Perry; Douglas, Shervington, Taumoepeau; Percival, Gillies; Betty, Kvesic, C. Jones.
Replacements: Pennell for Classens (74), Goode for Rasmussen (66), Arr for Perry (63), Lutui for Shervington (74), Abbott for Kvesic (14).Not Used: Currie, Tomaszczyk, Gulliver.
Referee: David Rose (RFU).