Full-back Delon Armitage was on song on Tuesday, with Booth describing his rousing performance as 'great' as Irish put themselves into third place in the table.
Centres Joe Ansbro, in the first half, and England ace Shontayne Hape after the break touched down for the Exiles, while young wing Tom Homer, the Premiership's leading points scorer, added 19 more with five penalties and two conversions.
Exeter were always chasing the game after Ansbro's try on three minutes, but showed their fighting spirit with Argentinian fly-half Ignacio Mieres kicking five penalties and converting a try from full-back Luke Arscott.
Mieres, though, was left shaken for a few minutes on the touchline when Armitage clattered into him, with an arm around his head, as the fly-half fielded the ball by his own 22.
Armitage only returned to action with Irish this month after a five-week ban for a dangerous tackle on Bath wing Tom Biggs and a concurrent ban for striking lock Dave Attwood with his knee in the same match on October 29. It was his fourth suspension in 2011.
But Booth said it was something and nothing, although officials may want to see it because of the player's troubled record.
The Irish coach said: "He went in for a tackle from behind and, as the player has bent down, he has gone up over the top of him. It is a penalty at most in my opinion.
"But, as always, because of what has gone before, people will have a closer look."
Chiefs head coach Rob Baxter said: "It certainly dazed him. There is definitely an arm over the top. That is not alleged, you can see that pretty clearly.
"The touch judge was in a pretty good position and he gave his worth on what he thought it was. I'm not too concerned about that, you just have to get on with it and play."
Irish were never comfortably ahead, even though they led 19-9 at half-time. Exeter, as they showed in beating Sale four weeks ago when losing by 16 points at the break, never give in.
Booth added: "We took our chances and I'm delighted about that. We started exceptionally well, we took the game by the scruff of the neck and the reason why we didn't dictate was probably because the penalty count was two-to-one in their favour.
"We have made life more difficult for ourselves than we needed to but make no bones about it, we are delighted with the outcome. We just could have been a bit smarter.
"What I would say about the contest is that there was a lot of endeavour from both sides and, from a crowd point of view, it would suggest to me that it was an enthralling contest. People were positive and that has to be good for everyone."
Baxter thought his men did well despite losing.
He said: "Ultimately, that first 20 minutes, we didn't play enough. In reality, we are a team which is learning.
"The only goal we gave ourselves this season was to be better. We came here last year and got nothing, now we have got a losing bonus point.
"We are just a better side when we go for it. My job is to free these guys up and make sure we go for it every week. By doing that, we will win more games than we lose."
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