Ben White capped a remarkable 15-point run with the decisive try as Exeter battled back to overcome a London Irish side whose long injury list gained two additions in a rugged encounter.
Exeter, kept going throughout by Gareth Steenson's kicking, scored both of their tries in the final 20 minutes, Dean Mumm's converted try putting them within a point of Irish and Ben White, taking them over the line. Steenson's second conversion carried his contribution to 19 points.
For the opening hour Irish were the better side, showing greater enterprise than a lethargic Exeter and with visitors' wing Tom James in the sin bin, the hosts looked set for victory, with tries from Nick Rouse and Marland Yarde and 13 points kicked by Ian Humhreys.
Irish, with 12 of their 35-man squad unfit, suffered two further injury blows and that ultimately told against them. When Topsy Ojo picked up a hamstring injury in the warm-up, resulting in Alex Lewington having a late call up, they might have thought then that it was not their day.
Exeter took an early lead with a penalty from Steenson after Yarde was penalised for crossing, but Irish had the better of the opening quarter as they attempted to move the ball at every opportunity. The visitors' defence was stretched but it was left to Humphreys to tie the scores with a penalty.
When Exeter were awarded another penalty, which Steenson kicked, the referee Andrew Small spoke to both captains in the hope of putting a lid on rampant ill-discipline. The players did not seem to heed Small's warning as Irish were again penalised allowing Steenson to kick his third goal.
After 28 minutes came the first real prospect of a try. After a close-range line-out, Halani Aulika appeared to drive over but the TMO ruled that excellent defensive work from Steenson and James Scaysbrook had held up the prop.
Irish were not to be denied for long as from the next scrum Rouse crashed over for a try, which Humphreys converted to give Irish the lead for the first time.
That lead should have been extended but Humphreys missed with a penalty after Tom Johnson was penalised for a dangerous challenge.
Just before half-time, Irish suffered another hammer blow when Aulika, their best player, was helped from the field with a leg injury.
Steenson put the Chiefs back in front with another penalty before Lewington made a neat break. The young full-back avoided Johnson's tackle and put Exeter under pressure, which forced James to commit a cynical foul by pulling back a support player. James was yellow carded and Humphreys kicked the penalty.
The game appeared to change dramatically in Irish's favour when immediately from the re-start, Bryn Evans, tore away on a 45-metre run to put the Chiefs on the back foot. The ball was recycled for Lewington to send Yarde in for the try, which Humphreys converted, before kicking a penalty for a 23-12 lead.
Back came Exeter, Jason Shoemark, appeared to have scored but his effort was ruled out by the TMO but Exeter got their reward when Steenson kicked his fifth penalty.
Irish had John Yapp yellow carded for dragging down a maul and Chiefs took full advantage by scoring their first try through Mumm with Steenson converting.
The lock Jebb Sinclair was another injury casualty for Irish before Exeter completed their comeback with the try by White, converted by Steenson.
London Irish Lewington; Yarde, Mulchrone (Stevens, 73), Sheridan, Fenby; Humphreys (Nimmo, 71), O'Leary (Allinson, 74); Parr (Yapp, 57), Paice (Geraghty, 73), Aulika (Halavatau, 34), Rouse (Nimmo, 44-47), Sinclair (Parr, 71; ), Danaher, Evanes, Treviranus.
Exeter Dollman; Whitten, Shoemark, Hill (Jess, 53), James; Stenson, Thomas (Lewis, 55); Sturgess (Moon, 53), Yeandle (Whitehead, 67), Tui (Rimmer, 56), Mumm, Welch, White (Hortsman, 75), Scaybrook, Johnson.
Referee Andrew Small.
Tries: Rouse, Yarde
Cons: Humphreys (2)
Pens: Humphreys (3)
Tries: Mumm, White
Cons: Steenson (2)
Pens: Steenson (5)