Lifeimi Mafi touched down for Munster and Parks pushed a penalty wide for Warriors.
The Tigers' tries came from Alesana Tuilangi, Ben Youngs and Steve Mafi with Toby Flood kicking 17 points.
Munster were the better team in the second quarter, with Simon Zebo and Lifeimi Mafi starting to pose a threat.
But a second try for Hamilton and late efforts from Manu Tuilagi and Mafi ensured Leicester had the final say.
The wing forced his way past Mafi only for O'Leary's superb covering tackle to force Vaughton into touch just short.
Munster centres Lifeimi Mafi and Sam Tuitupou produced some purposeful runs but Leinster's defence stood up to the visitors' opening barrage.
Mafi was then yellow-carded for a professional foul at a ruck, handing Parks the chance to reclaim the lead for the Warriors.
Shortly after, Munster wasted an overlap in the corner with Lifeimi Mafi and Denis Hurley stopped short with the try line at their mercy.
Dan Biggar had punished some French indiscipline to put the hosts in front but Wilkinson fed centre Mafi Kefu at the base of the scrum.
Munster started well, de Villiers winning a penalty on halfway and then setting up his centre partner Lifeimi Mafi for a jinking run into the 22.
Despite this setback, Barclay avoided Lifeimi Mafi's last-ditch tackle to race over for a breakaway try a minute later and Parks converted to put Glasgow 10-7 ahead.
Crane got his hat-trick after the break and Thomas Waldrom added a sixth before two Treviso tries, but Hamilton, Manu Tuilagi and Steve Mafi crossed late on.
The ball was beautifully spun through the hands of Barry Murphy, Earls, Lifeimi Mafi and Mick O'Driscoll before Warwick cantered in under the posts for a seven-pointer.
Lefeimi Mafi raced onto O'Gara's flat pass straight between Flutey and Fraser Waters, and a simple off-load put Tipoki in under the posts, giving O'Gara an easy conversion.
However, the centre then failed to regain his feet as he tried to wrestle the ball away from Peel and referee Wayne Barnes had no hesitation in sin-binning Mafi.
After half-time, Mafi was sin-binned after a high tackle on Rob Kearney but O'Gara kicked the 14 men back in front after Gordon D'Arcy had transgressed at a ruck.
Munster began to wear down the Glasgow defence and a brilliant surge by Rua Tipoki set up the equalising touchdown for centre partner Lifeimi Mafi 10 minutes from time.
Quick hands, swift pace and good running lines gave Lifeimi Mafi just enough space to squeeze in at the right corner flag, despite Lee Byrne's despairing tackle, for an unconverted try.
Another Munster score soon followed, the forwards driving to suck in the defence before the ball was spun wide to Mafi, who was stopped but popped the pass for O'Leary to shunt over.
His first chance came after 10 seconds as Lifeimi Mafi took out Olly Morgan as he chased the kick-off, but Paterson stunned the crowd by missing from straight in front of the posts from 30m.
Lifeimi Mafi was sin binned for kicking out in the 74th minute but Blues were unable to take advantage of their numerical advantage as they chased a try which could have earned them a bonus point.
Forward passes twice foiled attacking moves and then Keith Earls broke away after good work by Lifeimi Mafi but the full-back was penalised for holding on to the ball on the ground and the scoring opportunity was lost.
Jones, Mafi and Denis Hurley saw plenty of possession in the first quarter but Munster grew frustrated by the Dragons' well-organised, aggressive defence and O'Gara had to react sharply to prevent Ashley Smith from releasing a team-mate for the line.
Waldrom sat out the game's final minutes after killing possession, but he and his team-mates had done more than enough in the second half to end the contest comfortably in charge, underlined as Steve Mafi was driven over from close range.
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