The Cherry and Whites never panicked when they found themselves 16-12 down when Exeter hooker Simon Alcott scored the only try of a cracking match played on a slippery pitch and ending in pouring rain.
Fly-half Gareth Steenson had booted three penalties and converted Alcott's try, when the front row man finished off a multi-phased move inside the home 22 to touch down near the posts.
By that time, home fly-half Freddie Burns had kicked four penalties but, as the last quarter arrived and Exeter gave away kickable penalties, the Bath-born number 10 landed two more penalties, the decisive one seven minutes from time that gave Gloucester a seventh league win of the campaign.
It was a hard-fought victory that left Hogg happy.
The Scotsman said: "It was not a classic but there was lots of effort and lots of endeavour. You have two sides who have good characteristics and work ethic.
"It was a tight game that went back and forth but, in the last 20 minutes, we just managed to climb over the top of them.
"The defining characteristic of our side this season is that we have real resilience. That last 20 minutes when we were points down, we needed that in spadefuls. With the support behind us in a sell-out Kingsholm, we just had enough to do it.
"They are a very good side and have great consistency but we managed to match that over the 80 minutes and just did enough at the end.
"Great credit to numbers nine and 10 (Jimmy Cowan and Freddie Burns). It was never going to be a game where you were going to break out from your own end and score tries. It was about field position and was an arm wrestle and retaining ball.
"We got ourselves out there and we were able to get two or three phases together and got the resultant penalties off the back of it.
"Exeter are a good, physical side who work hard and retain the ball so, defensively, you have to man up."
Exeter Chiefs head coach Rob Baxter was animated with some of the decisions from referee Llyr Ap Geraint Roberts during the second half, but said he was pleased with his side who gained a losing bonus point as they now go into a mammoth mid-table clash next weekend with another West Country giant in Bath.
Baxter said: "I'm a bit disappointed that we didn't wrap the game up when we had the decisive moment of the match with the try. We created a little bit of daylight and we let Gloucester peg us back too easily.
"When we review the game, that will be the moment which we are probably most disappointed with.
"We made errors to put them in positions (to kick penalties) but let's remember we are away at Kingsholm against an in-form Gloucester side who put pressure on us and that pressure created penalties. Others were self-inflicted and other ones, I don't know where they came from.
"I said to the guys that one fixture never defines a season so to come here against an in-form Gloucester side and go away with a losing bonus point is still a very positive thing for us.
"We controlled some of the game but we didn't seem to get the rub of the green at times but that didn't stop us slipping bindings at scrums or making errors at line-out time. Those were errors we made which we have to stamp out if we want to come here and win."
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