Leeds fly-half Adrian Jarvis ended the match with 17 points
Relegation favourites Leeds picked up only their third win of the season as they edged out Exeter at Headingley.
A converted Hendre Fourie try and three penalties from Adrian Jarvis handed Leeds a 16-6 lead at the break, Gareth Steenson scoring for Exeter.
Bryan Rennie crossed early in the second half for Chiefs to reduce the deficit, but Leeds pulled away again with a touchdown from Alfie To'oala.
Jarvis then kicked a late drop goal to settle the home fans' nerves.
The former Bristol fly-half finished the game with a 17-point haul, with four penalties and a conversion alongside his drop-goal.
The win puts Leeds to within two points of second-bottom Newcastle, whom they face at Kingston Park next Saturday.
The importance of the result to Leeds was clearly evident in the opening exchanges, their reward coming in the 32nd minute as South Africa-born flanker Fourie crossed the Chiefs' line after a prolonged attacking spell.
Steenson responded with a second penalty shortly afterwards, reducing the home side's advantage to only 10 points by half-time.
A bright start to the second-period from Exeter led to a try for Rennie on 45 minutes following strong work by winger Nemani Nadolo.
A conversion from Steenson and third-penalty followed to bring the scores level at 16-16.
However, any hopes of a Chiefs comeback were dashed in the 65th minute, as To'oala put touched the ball down after a rolling maul.
Jarvis's drop-goal took the game further from Exeter's reach, with the visitors only able to muster a late drop goal from Steenson as they searched for a way back in.
Leeds head coach Neil Back:
"We'll do what we need to do or we will die trying - I believe we've got to win at least two of the next four games.
"Bearing in mind we've won three of the last 18, that's a big challenge.
"But without belief there is nothing. I 100% believe that we can go to Newcastle and win."
Exeter Chiefs head coach Rob Baxter told BBC Devon: "As far as I'm concerned we did enough dumb things to lose the game and that's why we've lost.
"They deserved to win it - we've got to take that on the chin and we've got to address why we lost.
"We've hit a little bit of a wall at the minute, I don't think it's anything to panic about but I think we've got to find our way through it now."
Replacements: Dollman for Rennie (64), Thomas for Poluleuligaga (63), Whitehead for Clark (41), Tui for Budgen (66), Gannon for Slade (66), Johnson for Phillips (45).
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