Brive (6) 13
Try: Vosloo Cons: Goode Pens: Goode 2
Leinster (19) 39
Tries: Kearney, McLaughlin 2 Cons: Sexton 2, Berne Pens: Sexton 5
Lions full-back Rob Kearney scored Leinster's opening try
Reigning champions Leinster got their Heineken Cup campaign back on track with victory over Brive in an uninspiring encounter in France.
English fly-half Andy Goode put Brive ahead but a try from full-back Rob Kearney and four Jonathan Sexton penalties put Leinster in charge.
Sexton added another penalty just after the break but Brive gave themselves hope with Gerhard Vosloo's try.
However, two late tries from Kevin McLaughlin sealed victory.
It was much-needed result for the Irish province, who suffered one of the surprise losses in the opening weekend at home to London Irish.
And it will banish the painful memories of their last visit to France, which saw them limp to an 18-15 loss to Castres last December.
They were too strong for an undisciplined Brive side containing a raft of Englishmen, including Goode, Jamie Noon and Steve Thompson, which did not have the guile to break through the visiting defence.
However, Leinster will leave France feeling that they missed a superb opportunity to claim a valuable try-scoring bonus point.
Goode and Sexton traded penalties in the opening 10 minutes before Leinster took control with a fine try from Kearney on 15 minutes.
Kearney cut a superb line to finish off a well-worked move involving Sexton, centre Brian O'Driscoll and a clever dummy run by Luke Fitzgerald.
Sexton extended the lead when Brive were penalised at a scrum and although Goode replied with his second kick, further indiscipline gave Leinster two penalties before the break.
The second half was a tetchy affair, with the referee's whistle preventing the game getting into any kind of rhythm.
Sexton made the score 22-6 just after the start of the second half and although Leinster wing Isa Nacewa was sin-binned on 49 minutes for a high tackle on Alexis Palisson, Brive could not take advantage of the 14 men.
Brive did reduce the deficit on 65 minutes when flanker Vosloo barged over after a spell of pressure but the home side were punished for an error from the kick-off.
From the back of a scrum, Leinster spread the ball wide with pace and Nacewa was released down the left wing after a neat pass from O'Driscoll.
The Fijian wing cut inside to feed McLaughlin and although Noon put in a brave last-gasp tackle, the substitute was just able to touch down.
Goode and O'Driscoll had a minor dust-up late on to keep the crowd interested and with the last move of the match, McLaughlin bundled over from the base of a scrum to complete the scoring.
Leinster coach Michael Cheika:
"I think hard work got us the game. There was not anything flashy or fancy, just a lot of good work.
"We backed ourselves a lot to throw the ball around when there were opportunities there.
"We didn't go into our shell, which we could have done because we knew what the implications were if we didn't win. That was good character."
Brive: Estebanez; Palisson, Noon, MacKay, Waqaseduadua; Goode, Perry; Kinchagishvili, Thompson, Barnard, Short, Browne, Vosloo, Forgues, Claassen.
Replacements: Cooke for Estebanez (70), Pejoine for Perry (54), Toderasc for Kinchagishvili (54), Idieder for Barnard (66).
Not Used: Bonrepaux, Uys, Azoulai, Orquera.
Leinster: R Kearney; Horgan, O'Driscoll, Fitzgerald, Nacewa; J Sexton, Reddan; Healy, Jackman, Ross, Cullen, Hines, O'Kelly, O'Brien, Heaslip.
Replacements: D'Arcy for Horgan (71), Berne for J Sexton (76), Fogarty for Jackman (46), van der Linde for Ross (61), McLaughlin for Cullen (54), Toner for Hines (70).
Not Used: McCormack, S Keogh.
Sin Bin: Nacewa (48).
Ref: James Jones (WRFU).