The Chiefs made two changes from the side that lost 12-9 at home to Bath, with James Hanks back in the second row in place of Peter Short while Bryan Rennie replaced Nic Sestaret in the centre.
Scotland flanker Richie Vernon returned to Sale's pack with James Gaskell switched to the second row in place of the injured Andrei Ostrikov.
The home side got the first points on the board after seven minutes as centre Jason Shoemark gave the final pass for full-back Phil Dollman to squeeze in at the corner.
Fly-half Ignacio Mieres was unable to add the touchline conversion but did add a penalty shortly after from close range.
Mieres kicked another penalty 12 minutes before half-time before the Chiefs then claimed their second try of the game.
After being held up over the line, number eight Richard Baxter picked up at the base of the scrum at the second attempt and found a gap to get over the line with Mieres adding the extras.
The Chiefs started the second half the stronger but were unable to turn the possession into points, but after a quick tap penalty they worked the ball wide through hooker Chris Whitehead before wing Matt Jess exchanged passes with Dollman.
Jess then found Sestaret, on as a replacement for Shoemark just before the interval, who went over for the third try, but the conversion from Mieres hit the far upright.
The Sharks pressed the Chiefs line where Baxter was shown a yellow card for a professional foul, but the seven-man pack forced Sale to concede a penalty and allow the home side to clear their lines.
Exeter claimed their second try-scoring bonus point of the season when Jess broke down the right before finding Dollman, but with wing Gonzalo Camacho outside the ball went back inside for Jess to touchdown.
The conversion attempt from Mieres hit the inside of the far upright before going over to give the Chiefs a 30-0 lead with 24 minutes left.
Exeter, now back to full strength, were then penalised close to their own line and after the kick to the corner replacement hooker Joe Ward was held up over the line.
But the visitors maintained the pressure which resulted in replacement centre Luther Burrell getting the touchdown.
Exeter were forced to play the final 10 minutes a man down when replacement prop Ben White was sent to the sin-bin, and the visitors took advantage of the extra man.
The Chiefs held the ball at the back of a ruck over their own line and referee Dean Richards deemed the ball was out, allowing replacement prop Tony Buckley to claim the touchdown which Nick Macleod converted.
However, there was still time for the Chiefs to push for a fifth try with a series of scrums under the posts leading to a penalty try which replacement Gareth Steenson converted.
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