A subsequent penalty from Ian Keatley had the visitors 17-7 ahead as half-time approached, but the Scarlets had the better of the second period as an Aaron Shingler try and Rhys Priestland's levelling 71st-minute penalty got them back on terms.
The result saw the Welsh region put to an end to their 14-match losing run against Munster in all competitions.
Mathematically the Scarlets can still reach the play-offs, but they will be almost certainly out of the running if Glasgow Warriors win in Treviso on Sunday.
For Munster, they picked up a welcome two points on the road and remain on course to face either table toppers Leinster or the Ospreys in the semi-finals.
The Scarlets - minus injured centres Jon Davies and Scott Williams - were under pressure in the early scrums with first-time starter Dave Kilcoyne acquitting himself well in the Munster front row.
The hosts were given a let-off when Keatley missed an eighth minute penalty from halfway, but a turnover in their own 22 produced a fine try for Nigel Davies' side.
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 Sean Lamont over for the converted score after 12 minutes.
But Munster showed their powers of recovery by scoring two converted tries in the space of five minutes.
A classy lineout steal from Mick O'Driscoll, in the Scarlets 22, saw Conor Murray ferry the ball on to Ryan and he needed no second invitation as he barged past half-backs Rhys Priestland and Travis Knoyle to score an opportunist try.
Keatley's conversion was swiftly followed by a try from winger Zebo. The out-half turned provider as his clever inside pass released the Corkman who managed to slip through for his seventh touchdown of the league run, with television match official Nigel Whitehouse confirming it.
Keatley and Priestland swapped penalties as Munster led 17-10 after half an hour's play.
A good period of Scarlets handling earned them a penalty but Priestland missed to the left of the target. Just before half-time play was help up for more than five minutes for an injury to Munster flanker Tommy O'Donnell who was carried from the pitch.
Munster, with Paul O'Connell putting in an energetic shift, had a golden opportunity to extend their seven-point interval lead but Keatley failed to pick up a loose ball just a metre from the Scarlets' whitewash.
He made some amends by kicking a 55th minute penalty to extend the Munster lead to 10 points after the Scarlets had been caught offside.
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 after being put through a gap by Stephen Jones.
Priestland converted to cut the visitors' lead to only three points, and the Welsh international was on target again with a 40-metre penalty to tie up the game.
Munster had to maintain their defensive shape and put their bodies on the line as the Scarlets tried to work a drop goal opportunity. However, pressure from O'Connell and company led to a couple of costly turnovers and a draw was probably a fair result in the end.
|Scarlets Score Card|
|Munster Rugby Score Card|