The Chiefs were ahead within the opening four minutes thanks to a Gonzalo Camacho try.
Gareth Steenson kicked the conversion and four penalties to open up a 19-point advantage for the home team.
An Andy Goode penalty got the Warriors off the mark just before half-time.
Two more violations by Exeter allowed the visitors to close the gap to 10 points with 12 minutes remaining.
Exeter's strong finish was aided by Worcester's Sam Betty receiving a yellow card in the 75th minute.