The Devon side outscored the Exiles two tries to one with all the visitors points coming from full-back Tom Homer as the visitors slipped to their sixth Aviva Premiership defeat in a row.
Exeter named an unchanged side from the one that beat Gloucester 28-27 last time out and were led onto the Sandy Park pitch by number eight Richard Baxter, who was making his 400th league and cup appearance for the club.
London Irish made two changes from the side that lost 41-32 at Leicester Tigers last Sunday with former England Saxon Adrian Jarvis starting at fly-half while Romanian international Paulica Ion was at tighthead prop.
The Chiefs applied the early pressure and fly-half Ignacio Mieres put the first points on the board with a 40-metre penalty.
London Irish levelled through a Homer penalty and after Mieres had missed one kick at goal, the fly-half succeeded with his next attempt to make it 6-3.
Baxter then made an excellent break down the left touchline before he was halted by flanker Matt Garvey, but the ball was worked across field and outside centre Bryan Rennie just failed to squeeze in at the left corner.
Referee Dave Pearson had already blown his whistle for a penalty on the opposite side of the pitch, but Mieres saw his attempt hit the far upright.
The Chiefs maintained the pressure with Rennie putting a neat grubber kick through forcing Homer to take the awkward bounce into touch five metres from his own line with half-time approaching.
Replacement hooker Neil Clark found Baxter to set up the the drive to the line and Hanks went over for his first try of the season from close range. Mieres added the conversion to give the Chiefs a 13-3 lead at the break.
Mieres, now kicking into the wind, missed an early opportunity to stretch the Chiefs lead with a 25-metre attempt, but it was the visitors who got the first points of the half.
A neat chip through from Jarvis and another awkward bounce caught two Chiefs defenders napping and allowed Homer to touchdown in the corner, although he was unable to add the touchline conversion.
Homer then reduced the arrears to two points with his second penalty but was just wide with his next attempt midway through the half.
That was just the jolt that Exeter needed and right wing Gonzalo Camacho crossed for his first try for the Chiefs having been initially tackled just short of the line.
Mieres missed the conversion and a 45-metre penalty before he was replaced by Gareth Steenson for the final 10 minutes.
With less than four minutes remaining the Exiles won a penalty 15 metres from the Chiefs line in front of the posts and they kicked to touch to set up a drive for a tense finish, but the Chiefs stood firm.
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