Gareth Steenson missed a last-gasp conversion to cost Exeter victory in a tight encounter with Gloucester.
The visitors played the final minutes with two men in the sin-bin and Exeter capitalised, driving over the line for Don Armand to score with seconds left.
But Charlie Sharples' second-half try and a Rob Cook penalty were enough for Gloucester, who had trailed 8-6 thanks to a Matt Jess score and Steenson kick.
The visitors leapfrog their opponents into eighth in the Premiership table.
With just four more games to go in the regular season, Gloucester are 13 points adrift of sixth place, leaving them with only faint aspirations of securing top-level European rugby next season. The Chiefs lie just a point behind them.
The sides traded penalty kicks early on in what was a scrappy encounter lacking quality. Cook kicked his second three-pointer to put his side 6-3 ahead before Jess shrugged off several tackles to squeeze over for his first try of the season.
Gloucester regained the lead five minutes after the restart through Cook's third penalty, which was quickly followed up with a try.
Experienced centre Mike Tindall and Cook linked up well to put wing Sharples in for an easy score in the corner.
Cook was off target with the conversion and a penalty to keep Exeter in the game, and in a tense final 10 minutes, Gloucester repeatedly gave away penalties, which ultimately saw replacement prop Sila Puafisi and flanker Sione Kalamafoni in the sin bin for needless infringements.
And with the time beyond the allotted 80 minutes, a powerful maul saw replacement forward Armand bundle the ball over the line but Steenson's conversion attempt strayed narrowly wide to leave Gloucester celebrating.
Exeter head coach Rob Baxter:
"It was great endeavour from the guys at the end but I am a little perplexed about how you can have a driving maul flying over the line that collapses and it is a yellow card but not a penalty try, especially after a couple of penalties that led up to it.
"It was tough for Gareth because he hadn't had any shots at goal at that point and there was a very tough wind. Gareth missing a kick is not a big issue for me - it's a bit more how we needed a conversion in the last seconds to win the game.
"I am not going to hide my disappointment because I don't think that we played particularly well. I said to the guys afterwards that if you want to win Premiership games you have to go out there and play really well."
Gloucester director of rugby Nigel Davies:
"That was our third Premiership on the trot - that is pretty significant, so I was pleased about that. We had really targeted this one as a key game in our season.
"It can almost turn round our season a little bit. Exeter are having a great season and rightly so get a lot of plaudits, but right now we sit above them in the league.
"We have had a tough season. We've been nowhere near where we would have liked to have been.
"But we are still battling and to get three wins on the bounce - and come up from where we have been - is pretty significant and the boys should take a lot of credit for that."
Exeter: Arscott; Vainikolo, Whitten, Dollman, Jess; Slade, Lewis; Moon, Yeandle, Tui, Mumm, D Welch, Ewers, Johnson, Horstmann.
Replacements: Hill for Arscott (52), Steenson for Slade (60), Rimmer for Moon (64), L Cowan-Dickie for Yeandle (35), Armand for Tui (56), Brown for Horstmann (56).
Not Used: Scaysbrook, Thomas.
Gloucester: Cook; Sharples, Tindall, Twelvetrees, May; Mills, Cowan; Wood, Dawidiuk, Knight, Stooke, James, Kalamafoni, Kvesic, B Morgan.
Replacements: Trinder for Tindall (59), F Burns for Mills (45), Knoyle for Cowan (65), Y Thomas for Wood (64), Britton for Dawidiuk (41), Puafisi for Knight (54), Lokotui for James (60).
Not Used: G Evans.
Sin Bin: Puafisi (77), Kalamafoni (79).
Referewe: Matthew Carley (RFU).