Exeter secured back-to-back Aviva Premiership wins on a bitterly cold day at Sandy Park to leave Leeds still looking for their first win of this campaign.
Ryan Davis, in his first season with the Chiefs, landed five penalties from his six attempts to take the Devon side up to sixth place in the table.
Exeter boss Rob Baxter made four changes from the side that drew last time out against LV= Cup opponents Cardiff Blues, recalling wing Andrew Higgins, centre Bryan Rennie, prop Chris Budgen and flanker James Scaysbrook.
Leeds, still without a Premiership win this season, went in to the game without key forwards Steve Thompson and Hendre Fourie, both on England duty against Samoa at Twickenham.
The two sides have met on two previous occasions at Sandy Park in the old National Division One with the Yorkshiremen having won on both occasions.
Fly-half Davis put the Chiefs ahead with two penalties in the opening 10 minutes, the first being a 30-metre penalty from close to the left touchline, while the second was from 42 metres in front of the posts.
The home side dominated the early passages and it was not until midway through the half that the visitors mounted their first serious attack.
From a 15-metre ruck in front of the posts Leeds worked the ball to the blindside and centre Henry Fa'afili was stopped close to the line. Chiefs won the ball at the turnover and cleared their line before Leeds were penalised at their lineout to ease the pressure further on the Exeter line.
Their next attack also faltered when centre Scott Barrow gave a grubber kick to the left corner but it was too long for wing Peter Wackett as Andrew Higgins patiently waited for the ball to go over the line for a 22 metre drop out.
Leeds skipper Marco Wentzel tried his speed down the left touchline but his chip ahead was too hard and then fly-half Ceiron Thomas saw his 35 metre penalty attempt hit the left upright.
With two minutes of the half remaining Chiefs were penalised for a late tackle by wing Mark Foster on full back Michael Stephenson and Thomas found the gap between the posts to leave them trailing 6-3 at the break.
Leeds should have scored the first try of the game ten minutes after the restart but the hosts defended stoutly only for the visitors to level with a simple Thomas penalty from in front of the posts.
Exeter had an opportunity to hit back immediately but the penalty attempt from Davis, from out on the left just outside the 22, scraped past the near upright. His next attempt midway through the half, from out on the right, put the home side ahead again.
Thomas missed another penalty attempt five minutes later but then Exeter went on the attack with the forwards drive held-up over the line. After three attempts at the scrum Leeds were penalised and Davis stretched the Chiefs lead.
The confidence in the Exeter side grew as the stepped-up the tempo as the game went in to the final ten minutes. Davis kicked his fifth penalty of the game leaving the visitors needing to score twice to snatch the game.
With two minutes remaining Thomas slotted a long range penalty to give Leeds a much needed loosing bonus point but still rooted to
the foot of the table.
Exeter: 15 Luke Arscott, 14 Andrew Higgins, 13 Phil Dollman, 12 Bryan Rennie, 11 Mark Foster, 10 Ryan Davis, 9 Haydn Thomas, 8 Richard Baxter, 7 James Scaysbrook, 6 Tom Johnson, 5 James Hanks, 4 Tom Hayes (capt), 3 Chris Budgen, 2 Simon Alcott, 1 Brett Sturgess.
Replacements: 16 Chris Whitehead, 17 Ben Moon, 18 Hoani Tui, 19 Dave Gannon, 20 Chad Slade, 21 Garrick Cowley, 22 Ignacio Mieres, 23 Jason Shoemark.
Leeds Carnegie: 15 Michael Stephenson, 14 Lee Blackett, 13 Henry Fa'afili, 12 Scott Barrow, 11 Peter Wackett, 10 Ceiron Thomas, 9 Scott Mathie, 8 Daniel Brown, 7 Rhys Oakley, 6 Kearnan Myall, 5 Marco Wentzel (c), 4 Tom Denton, 3 Juan Gomez, 2 Phil Nilsen. 1 Gareth Hardy.
Replacements: 16 James Parkes, 17 Miguel Alonso, 18 Phil Swainston, 19 Danny Paul, 20 Alfie To'oala, 21 Warren Fury, 22 Lachlan MacKay, 23 Leigh Hinton.
Referee: Dave Pearson