Munster looked good for the win at 20-10 up until Aaron Shingler's try on 61 minutes got Scarlets back into the match and, after Priestland had expertly levelled things up, the Welsh region went hell for leather for the win but fell short.
The home side's determination to overturn their losing streak against Munster was obvious from the start at Parc y Scarlets.
After seeing Munster fly-half Ian Keatley's early penalty go wide they took the lead with a sensational try from left wing Sean Lamont.
Scrum-half Gareth Davies started the move inside his own 22 with Liam Williams, George North, Stephen Jones, Shingler and Matthew Rees all getting their hands on the ball in a move that culminated in the Scottish wing going over for a converted score.
But Munster are chasing a second consecutive title and responded with two tries inside four first-half minutes.
Lock Donnacha Ryan crossed on 17 minutes after the Irish province stole a lineout on the Scarlets' throw, ten metres from the try line. Scrum-half Conor Murray fed Ryan and the big second-row ploughed through the home side's flailing tacklers.
The score gave Keatley the chance to atone for his earlier miss with a conversion, and he then set up wing Simon Zebo who touched down for his seventh league try of the season.
Keatley added the extras and then slotted a penalty to put Munster firmly in charge in south Wales.
Priestland could have brought the Scarlets to within a whisker of the champions but where he succeeded with his first attempt on goal he failed with his second, making it 17-10 at half-time.
Keatley restored Munster's ten-point cushion five minutes after the break with a coolly taken penalty.
But then the home side gave themselves a lifeline in the match, and of making the semi-finals, when Stephen Jones pulled two Munster defenders onto him and slipped the ball to a charging Shingler and the flanker ran over from 22 metres out.
Priestland converted and with ten minutes to go he had a chance to level the scores from 40 metres out.
Buoyed by the always-vocal home support, Wales' new pin-up boy calmly put it through the posts.
The Scarlets were on a mission and trusted their chances to the off-load game. Forwards and backs all combined around the fulcrum of Jones, who popped up everywhere.
But while there was no doubting intentions, their execution in a gripping finale was lacking as they could not find the killer pass and both teams were ultimately left frustrated.
|Scarlets Score Card|
|Munster Rugby Score Card|