Fly-half Gareth Steenson booted 22 points and Exeter plundered five tries as they crushed London Welsh to end a run of five Aviva Premiership matches without a win.
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The Chiefs stay eighth and London Welsh are now just three points above bottom-of-the-table Sale Sharks.
The home side opened a comfortable 19-9 lead at the break thanks to four penalties from Steenson and his conversion of the only try of the half, which came from hooker Jack Yeandle.
Gavin Henson replied with three penalties, but the visitors were put to the sword in the second half.
Turther tries from skipper Tommy Hayes, Damian Welch, Sireli Naqelevuki and Jack Nowell, all converted by Steenson, steered the Devon side to their deserved bonus-point victory.
Neither side had won in their last five league outings heading into the contest, while the Exiles had not tasted victory at Exeter since a National One clash in October 2000.
The opening 15 minutes was littered with six penalties, with four of them from kicking positions. Former Wales and Lions international Henson landed two for the visitors, with opposite number Steenson matching him.
Midway through the half London Welsh open-side flanker Julio Farias Cabello was warned by referee Andrew Small for a tackle on full-back Luke Arscott off the ball, and Steenson put the Chiefs ahead with his third kick.
Yet more penalties followed, both sides at fault. Henson levelled from wide on the right only for Steenson to immediately restore the advantage.
The visitors lost hooker Neil Briggs just before the half hour to an arm injury, and he was replaced by former Plymouth Albion prop James Tideswell. The Chiefs went close to scoring but the maul was pulled down.
The penalty was kicked to touch and the forwards drove over the line for Yeandle to score the opening try of the game from close range. Steenson converted to give the Chiefs their 10-point interval cushion.
The Chiefs came out fired up for the second half and early pressure paid off when open-side flanker James Scaysbrook gave a long overhead pass to skipper Hayes who squeezed in at the corner.
Steenson converted from the touchline but Exeter were briefly pegged back when Canada wing Phil MacKenzie darted over for London Welsh. Henson's conversion reduced the arrears to 10 points again.
The Chiefs wasted no time building their lead again as centre Jason Shoemark fed Damian Welsh, who had been on the for just seven minutes as a replacement for lock Dean Mumm, to touch down out wide. Steenson again added the extras.
One of the biggest cheers from the 7,317-strong crowd came 13 minutes into the second half and at the expense of referee Small who had to leave the field due to an injury to be replaced by Championship referee Darren Gamage, who had been the fourth official.
Exeter's third try-scoring point of the Premiership season came after 57 minutes when Arscott gave the pass to outside centre Naqelevuki who shrugged off a half tackle to stretch for the line, and Steenson converted.
The Chiefs defence was again tested but it stood firm in the closing 15 minutes. Exeter went in search of a fifth try which came six minutes from time as wing Nowell raced in from 35 metres and Steenson converted.