But realistically the Scarlets needed a victory at Parc y Scarlets to keep alive their hopes of securing a Pro12 play-off place for the first time.
The draw consolidates Munster in third place while the Scarlets are in fifth on the same number of points as Glasgow, who play in Treviso on Sunday.
The Scarlets and Munster scored two tries each. Sean Lamont and Aaron Shingler went over for the Scarlets with Donnacha Ryan and Simon Zebo scoring for Munster.
A turnover in Scarlets 22 produced a fine try for the Welsh region. George North, who passed a late fitness test on a groin injury, made the initial burst before the ball was recycled with captain Matthew Rees putting Lamont over for the converted score on 11 minutes.
Munster showed their powers of recovery by scoring two converted tries in the space of five minutes. First the Scarlets conceded a soft try when they failed to stop Ryan from a line-out with Keatley's conversion making it 7-7 on 17 minutes.
And almost immediately the visitors were in the lead after a fine inside pass from Keatley put Zebo in, although the score was only awarded after the intervention of the Television Match Official Nigel Whitehouse.
Keatley and Priestland swapped penalties as Munster led 17-10 after 30 minutes.
Munster had a golden opportunity to extend their lead after the interval lead but Keatley failed to pick up a loose ball just a metre from the Scarlets line, though the outside-half made some amends by kicking a 55th minute penalty to make it 20-10.
But just as Munster looked as if they were going to shut the game out, the Scarlets got some momentum together with Shingler skipping past two tackles to score their second try, and Priestland converted. Priestland was then on target to kick a 40-metre penalty after 71 minutes to tie the scores at 20-20.
Matthew Jarvis landed a monster penalty with the last kick of the game to guide Connacht to a smash-and-grab 19-16 win over Italian side Aironi.
Connacht were below par for much of this RaboDirect PRO12 tie at the Sportsground, trailing 16-3 at one stage due to a Quintin Geldenhuys try and some fine place kicking from Luciano Orquera.
Aironi were gunning for their first ever away victory, but Connacht tallied up 16 points in the final quarter - including a try from Rodney Ah You - to boost their hopes of a best-ever league finish of eighth.