Trump hit two century breaks in the last two frames to claim a 6-4 victory after Murphy fought from 3-1 down after the interval to level proceedings at 4-4.
But it was an incident in the fourth frame that sparked mayhem in the Ally Pally arena.
MASTERS SNOOKER RESULTS LIVE: LATEST SCORES FROM ALEXANDRA PALACE
A wasp made its way into the playing area as Murphy was assessing his options on the baize.
It chased the Magician around the table before he used his cue and a cloth to try and swipe it away.
In the aftermath Murphy revealed he has a terrible fear of the flying insect and was critical of the fact such a major disruption was allowed to happen in such an important event.
He said: “I’m terrified of wasps! Who isn’t? What are they for? Why are they here?
“Why they’re in that room I’ve got no idea, it’s one of the problems of playing in buildings like this – they’ve got holes everywhere.
“There’s wildlife in this building that perhaps shouldn’t be here so liqueur paint wouldn’t do any harm. A bit of money being spent would seal that up.
“We shouldn’t have things like that causing distractions on an indoor sport.”
Trump’s win sets up a semi-final clash against Kyren Wilson guaranteeing a maiden finalist at this year’s Masters.
Speaking about the loss to Trump, Murphy added: “He showed his class in the end. He’s an incredible scorer.
“I just couldn’t get ahead. I had a couple of chances to get on top and I didn’t take them.”