A solid start for Edinburgh Rugby saw them hold off the Leinster attack for the first half hour before the visitors picked up speed and earned a bonus-point win at Murrayfield.
The hosts did well to match their opponents for the early part but a double blow - inflicted by a penalty try and yellow card to David Denton - was followed up by another score with the man advantage.
A Piers Francis drop-goal was on the only second-half response before Leinster secured the bonus-point with a pair of scores.
Edinburgh prop Willem Nel then gave the crowd the something to celebrate as the tight-head produced a lovely finish from 40 metres out to score his third of the season, five minutes before the final whistle.
Edinburgh Rugby head coach Michael Bradley, said: "The critical period was the combination of the yellow card, the penalty try and the score conceded when we were a man down but ultimately they had too much power for us.
"We competed in patches against a very good Leinster side, that is a quality outfit, but it wasn't enough.
"The crowd were fantastic tonight. That, combined with the Willem Nel try are the immediate positives we can takes from this match but we have to take the chances that we create - Leinster were much better at doing that than us tonight."
Early pressure from the visitors saw the action move perilously close to the Edinburgh line but the first of many good clearance kicks from wing Dougie Fife kept the home side out of danger.
A great kick to touch from Matt Scott precipitated another lineout on halfway and as Leinster surged again, before more good clearance work from Fife.
A great break, headlined by full-back Greig Tonks and Scott_ from turnover ball, but it came to to nothing when a knock-on from Allan Jacobsen stalled the run.
With Leinster back-row Kevin McLaughlin penalised at the scrum, Edinburgh opted for the penalty kick 30m in front of the posts, which Laidlaw slotted easily to put Edinburgh ahead after 18 minutes (3-0).
Less than two minutes later a high tackle from Jacobsen on O'Driscoll saw Sexton line up his penalty from a similar distance and it sailed between the uprights to even the scores before he missed the opportunity to extend the lead with an effort awarded after Denton was pinged for not releasing.
As composures began to go, both sides started to make errors with spilled passes and knock-ons.
A somewhat harsh yellow card for Denton - penalised for coming in from the back of a Leinster maul - saw referee Ian Davies also award the opposition a penalty try, which Sexton slotted to 3-10 with five minutes left in the half.
With Edinburgh a man down, Leinster grabbed the game by the scruff of the neck and, moments later, centre Gordon D'Arcy went over the whitewash, the try converted by Sexton.
As the seconds ticked down to half time, however, Edinburgh rallied and as back-row Sean O'Brien ploughed into an Edinburgh ruck, the hosts were awarded a penalty, which Laidlaw duly slotted.HALF-TIME
: Edinburgh Rugby 6-17 Leinster
Edinburgh centre Atiga was replaced by James King as Edinburgh went into the second half with fourteen men, though managed to fend off any further scores form the Heineken Cup holders until Denton's returned.
Edinburgh then suffered two major setbacks in a matter of minutes as back-row Stuart McInally and winger Tim Visser left the field with a head knock each to be replaced by Roddy Grant and Sep Visser respectively.
As the Leinster pack advanced, Francis seized the opportunity for a drop goal, successfully clearing the uprights as Edinburgh narrowed the gap (9-17).
Having put in a tough shift, Georgian internationalist Dimitri Basilaia was replaced by Perry Parker before Shane Jennings carved through the Edinburgh midfield, passing to Sexton who crossed and scored for Leinster's third try, which he converted to make it 9-24.
Positive running, tackling and good work at the breakdown came to nothing for Edinburgh during the next phase of play as a sustained period of attack five metrea from the Leinster line was halted when their number 8 Jamie Heaslip was yellow carded for killing the ball, giving Edinburgh the advantage of the extra man.
The chance was squandered, however, with a overly long throw in the ensuing lineout from Lawrie. Leinster then took charge and crossed the line moments later as Madigan touched down, following a great break from O'Brien, the bonus point try converted again by Sexton to put the visitors out of reach (9-31).
With five minutes to go, however, the home side gave the support plenty to cheer about as Nel sidestepped Jennings and powered past Conway and Reddan, taking the latter over the line with him for a well-worked try, converted by Francis before Nel continued off the pitch to a standing ovation to be substituted by Cross.
Edinburgh continued with their second wind, if too late, in the closing minutes as they battled the Leinster defence but a lineout to the visitors saw Sexton win the ball which he kicked into the stands as the clock ticked over to 80.FULL-TIME
: Edinburgh Rugby 16-31 Leinster
15 Greig Tonks; 14 Dougie Fife, 13 Matt Scott, 12 Ben Atiga, 11 Tim Visser; 10 Piers Francis, 9 Greig Laidlaw CAPTAIN, 1 Allan Jacobsen, 2 Andy Titterrell, 3 Willem Nel, 4 Grant Gilchrist, 5 Sean Cox, 6 Stuart McInally, 7 Dimitri Basilaia, 8 David DentonSubstitutes
: 16 Steven Lawrie on for Titterrall (62'), 17 Robin Hislop on for Jacobsen (62'), 18 Geoff Cross on for Nel (77'), 19 Perry Parker on for Basilaia (55'), 20 Roddy Grant on for McInally (47'), 21 Richie Rees on for Laidlaw (74'), 22 James King on for Atiga (41'), 23 Sep Visser on for Tim Visser (48')Leinster:
15 Rob Kearney, 14 Fionn Carr, 13 Brian O'Driscoll, 12 Gordon D'Arcy, 11 Luke Fitzgerald, 10 Jonathan Sexton, 9 Eoin Reddan, 8 Jamie Heaslip, 7 Sean O'Brien, 6 Kevin McLaughlin, 5 Devin Toner, 4 Leo Cullen (c), 3 Mike Ross, 2 Sean Cronin, 1 Cian Healy. Replacements
: 16 Aaron Dundon, 17 Heinke van der Merwe, 18 Michael Bent, 19 Tom Denton, 20 Shane Jennings, 21 Isaac Boss, 22 Ian Madigan, 23 Andrew Conway.
Referee: Ian Davies (WRU, 7th competition game)
Assistant Referees: Peter Allan, Bob Nevins (both SRU)
Citing Commissioner: Paul Minto (SRU)
TMO: Jim Yuille (SRU)
RaboDirect PRO12 Man of the Match: Sean O'Brien