It left Scarlets coach Nigel Davies ruing what might have been, but full of praise for the pride and effort displayed by his team.
"It was a great performance and I really thought we should have won the game. We played all the rugby but we conceded two soft tries," said Davies.
"We will kick ourselves for that. But this performance shows how far we have come in a short time that we can come to a place like Munster and feel we should have got more out of the game.
"We are bitterly disappointed not to have got a win and bar those two stupid defensive lapses we would have."
Edwards' first try helped the Scarlets draw level at 13-13 on the stroke of half-time and then Rhys Priestland landed a penalty three minutes after the break to grab the lead. But the visitors then failed to take advantage when Munster had back row man Tommy O'Mahony sent to the sin-bin.
But while the flanker was kicking his heels on the touchline he saw his side take a commanding lead as the centre pair of Sam Tuitupou and Barry Murphy bust through the Scarlets' defence to streak clear for tries which Paul Warwick converted to give the league leaders a 11 point advantage.
The Scarlets recovered their poise when Edwards crossed at the posts for his second try and Priestland's conversion and later penalty set up a thrilling finish.
Stoddart created the opportunity to win the game with a great break, but when he took the return pass from Regan King he got caught from behind and ignored Evans on his right.