The hosts dominated much of the first half and were 12-3 up at the break thanks to four penalties from the boot of fly-half Gareth Steenson, with the Exiles' only reply coming through a Tom Homer penalty.
Steenson added a fifth penalty early in the second half and, although his opposite number Ian Humphreys replied with one of his own, Exeter crossed the whitewash twice through wing Matt Jess and replacement Dave Ewers with Henry Slade converting the latter score.
The Chiefs made two changes to their starting line-up from the side that won 24-18 at Worcester last time out. Brett Sturgess replaced Carl Rimmer at loosehead prop while Ben White at blindside flanker in place of Ewers.
London Irish, who have won just once on the road this season, knew a win would consign London Welsh to a quick return to RFU Championship rugby next season with three games remaining - starting with tomorrow's home clash with Northampton.
Wing Topsy Ojo and openside flanker Jebb Sinclair returned after being rested for the Exiles' 33-point draw at home to Sale two weeks ago. There was also starts for scrum-half Darren Allinson and tighthead prop Leo Halavatu.
All bar one brief lone voice in the near-9,000 crowd observed the minute's silence before kick-off in memory of former Prime Minister Margaret Thatcher, who died on Monday.
The Chiefs opened the scoring after 15 minutes with Steenson, who had hooked a 35-metre kick five minutes earlier on a very heavy pitch, landed a penalty from just inside the Exiles' half.
London Irish hit back but, with a strong breeze in their faces, kicked two penalties to touch. But the Chiefs were penalised after the second lineout for not releasing at the tackle so Homer levelled the scores midway through the half.
The Exiles should have gone back in front in the final 15 minutes of the half but squandered a couple of opportunities - one just two metres from the line - through unforced errors.
With the visitors being forced to defend their line, some indiscipline crept into their game, which resulted in Steenson kicking three penalties in the final 10 minutes of the half to give the Chiefs a 12-3 interval lead.
Having controlled the opening 10 minutes of the second period, Steenson slotted the first points of the half with a 30-metre penalty.
Just before the hour mark, London Irish fly-half Humphreys pulled three points back for the visitors, but the Chiefs hit back immediately.
A maul drove the Exiles back 25 metres before they pulled it down illegally. With advantage being played, Exeter scrum-half Haydn Thomas fed Steenson, who flicked the ball for Jess to touch down.
Steenson's touchline conversion - his second attempt after an early charge - fell short of the target.
The Exiles had an opportunity to pull back another three points but decided to kick to the corner and the Chiefs were able to defend the lineout.
Ewers then bulldozed his way over the line from close range for a last-minute try which was converted by replacement fly-half Slade - three minutes into his Premiership debut.