Edinburgh took an early lead through Visser's first two tries but fly-half Ian Keatley and wing Luke O'Dea pegged them back with a try apiece before Keatley secured victory with a 69th-minute penalty.
Visser got his third late on to prove that his appetite for the tryline remains as voracious as ever despite his summer exertions playing in the blue of Scotland.
The Dutch-born speedster cut his teeth on the international scene on tour in Samoa and Fiji scoring two tries on his debut.
He also scored 13 tries to top the RaboDirect PRO12's try scoring charts for a third year running last season but after the Munster match, thoughts of a fourth successive crown were far from his mind.
"Munster shouldn't have won this game," said Visser.
"They played half the game we did but compared to last year we have made huge progress.
"We dominated physically and we are putting good phases together but just our inability to keep hold of the ball at crucial moments meant we lost this game.
"It's hugely frustrating because we dominated them physically in the contact.
"They (the tries) were all good, it's good just getting what I can from the players around me.
"They are putting me away which helps and I am always happy to finish things up."
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