Tom Homer provided all the points for the visitors, including a try in the second-half that gave his team hope of a comeback.
However Exeter - who touched down through James Hanks and Gonzalo Camacho - held firm till the final whistle to make it six wins from seven and boost their chances of finishing in the top four.
The Chiefs have been the Premiership's surprise package this season and they continued their impressive form in the first half, leading 13-3 at the break.
Hanks went over to go alongside eight points from the boot of Ignacio Mieres, with Homer responding for the visitors.
And although Irish mounted a brief revival through Homer's try and a further penalty but Camacho's touchdown confirmed Exeter's victory.
Irish, by contrast, have suffered a slump in form losing their last five domestic encounters, and their lack of confidence was exposed in the first period.
Mieres opened the scoring with a penalty after seven minutes, although Homer responded for the visitors with one of his own.
However, the Argentinean struggled with the boot, missing five of his eight attempts, but he did regain their advantage in the 21st minute with a second three-pointer.
As always the hosts' game was based around their powerful pack and, after several drives close to the away side's line, Hanks eventually powered over from close range, Mieres converting.
The second half initially continued in the same vein, but Irish managed to get themselves back into the game when the ball fell kindly for Homer to touch down.
The same player missed the conversion before adding a penalty to reduce the deficit to two points. But the Chiefs showed that they are made of stern stuff as Camacho's try sealed the win.
London Irish: Homer; Yarde, Ansbro, Shingler,Tagicakibau; Jarvis, Allinson; Corbisiero, Paice, Rautenbach, Kennedy (capt), Evans, Danaher, Garvey, Gibson.
Replacements: Buckland, Lahiff, Ion, Casey, Gray, Treviranus, Armitage, Hodgson.