Ian Madigan grabbed Leinster's second try, converted byJonathan Sexton, who added a penalty for a 20-11 lead before Ronan O'Gara replied with three points of his own before half-time.
Another Sexton penalty and O'Driscoll's try, confirmed by the TMO, appeared to have put the contest to bed with Sexton converting to make it 30-14 after 56 minutes.
But Conor Murray scored an opportunistic try in the left-hand corner which was converted by substitute kicker Ian Keatley as Munster put the pressure on, though Leinster held firm for the final 13 minutes.
Leinster made a blistering start with man-of-the-match Eoin Reddan feeding Strauss who charged forward and managed to squirm his way through the Munster defence before touching down while on his back after nine minutes.
Jonathan Sexton added the extras but Munster came roaring back three minutes later, as Mike Sherry found Simon Zebo who cleverly offloaded while on his knees to O'Mahony who touched down, O'Gara missing the conversion.
Munster came straight back though and gained an advantage with O'Gara skewing an attempt at a drop goal though it came back for the penalty on the '22 which he dispatched for an 8-7 lead after ten minutes.
Three minutes later Sexton landed a penalty from 45 metres out before Kevin McLaughlin had to go off with a wrist injury, replaced by Jordi Murphy.
O'Gara missed another drop goal attempt before play went back for a penalty, which he put away for an 11-10 lead to Munster after 14 minutes.
Strauss then came close to getting his second try before Ian Madigan stepped inside Casey Laulala and slid over despite O'Gara clinging onto his ankles.
Sexton put his conversion through the posts to make it 17-11 six minutes before the half hour, though his penalty soon after from 45 metres dropped narrowly short, but he made amends soon after with another for a nine-point lead.
Back came Munster when Strauss was penalised for going off his feet, O'Gara making no mistake to make it 20-14 at half time.
Donnacha Ryan then went in from the side allowing Sexton to bend his kick over for a 23-14 lead and the first score of the second period.
Fergus McFadden and Strauss then charged up the middle before play spread to the left, with Madigan expertly finding O'Driscoll who stayed strong to touch down despite pressure from Denis Hurley, with the TMO confirming the try.
Sexton's conversion from the left was good and Leinster were now 30-14 ahead after 56 minutes, with substitute Damien Varley shown a yellow card for his actions during the play.
Sean Cronin came on for Strauss who left the field to a loud ovation before O'Gara was replaced by Keatley with 20 minutes left.
The pitch began to take its toll with O'Driscoll taken off with an ankle injury while Andrew Conway was soon stretchered off after taking a knock to his face from Zebo's leg.
With 13 minutes left though Munster stole the ball from a rolling Leinster maul and set up a ruck for Murray to capitalise on the unguarded blindside and go over in the left-hand corner, Keatley kicking the conversion from the touchline to make it a nine-point game.
Munster poured forward again from an attacking lineout, with Keatley finding Keith Earls, but a controversial call ruled his pass to Laulala had gone forward, denying him a try, as Leinster held on to seal victory.
|Leinster Rugby Score Card|
|Munster Rugby Score Card|