Leinster too good for Chiefs
Leinster too good for ChiefsSHARE
Leinster went ahead after a tight first quarter when Johnny Sexton started the move with a delightful cross kick which eventually saw the flyhalf cross from the breakdown on the blind side for the game's opening try.
The Chiefs' Gareth Steenson and Sexton then struck penalties to give the visitors a five-point advantage at the break before the home side drew level when Steenson fed winger James Short for their only try to level matters at 8-8.
Leinster finished the stronger in the final quarter though with captain Isa Nacewa edging Leinster back in front before Conan's late match winner.
The win takes Leinster six points clear at the top ahead of next Saturday's return at the Aviva Stadium. Exeter and Montpellier are level on eight points in second and third place respectively.
Leinster ended a run of 17 unbeaten games for the Chiefs at Sandy Park stretching back almost a year.
Tries: Sexton, Conan
Pens: Sexton, Nacewa
Exeter: 15 Phil Dollman, 14 James Short, 13 Henry Slade, 12 Ian Whitten, 11 Olly Woodburn, 10 Gareth Steenson (captain), 9 Nic White, 8 Thomas Waldrom, 7 Matt Kvesic, 6 Don Armand, 5 Jonny Hill, 4 Mitch Lees, 3 Harry Williams, 2 Luke Cowan-Dickie, 1 Alec Hepburn.
Replacements: 16 Jack Yeandle, 17 Ben Moon, 18 Tomas Francis, 19 Sam Skinner, 20 Sam Simmonds, 21 Will Chudley, 22 Sam Hill, 23 Jack Nowell.
Leinster: 15 Rob Kearney, 14 Fergus McFadden, 13 Garry Ringrose, 12 Robbie Henshaw, 11 Isa Nacewa (captain), 10 Johnny Sexton, 9 Luke McGrath, 8 Jack Conan, 7 Sean O’Brien, 6 Rhys Ruddock, 5 Scott Fardy, 4 Devin Toner, 3 Tadhg Furlong, 2 Sean Cronin, 1 Cian Healy.
Replacements: 16 James Tracy, 17 Jack McGrath, 18 Michael Bent, 19 James Ryan, 20 Josh van der Flier, 21 Jamison Gibson-Park, 22 Ross Byrne, 23 Jordan Larmour.
Referee: Romain Poite (France)
Assistant referees: Cyril Lafon (France), Stéphane Boyer (France)
TMO: Éric Gonthier (France)