Scarlets (3) 16
Tries: Daniel Con: S Jones Pens: S Jones 3
Ulster (13) 16
Tries: Humphreys, Wallace Pen: Humphreys Drop-goal: Humphreys
Scarlets' Stephen Jones is halted by Andrew Trimble and Stephen Ferris
The Scarlets remain winless in 11 successive Heineken Cup games after this draw in dire conditions at new home Parc y Scarlets.
The visitors led 13-3 at the break through Ian Humphreys' drop-goal, his try and another by Paddy Wallace.
Stephen Jones' kicking and a Darren Daniel try brought the hosts back into the game after the break.
But Humphreys' and Jones' kicking duel continued to the death as both sides failed to claim victory.
The hosts' miserable European campaign continued in the opening 40 minutes in the dreadful conditions.
Stephen Jones' kick-off epitomised the Scarlets' season thus far - off kilter as the ball ran dead, bringing a scrum on half-way at which the Wales fly-half must have been relieved to see a free kick awarded against Ulster.
Jones later sent a clearance over the dead-ball line as he sought to take advantage of the wind at his back.
But those were rare blips from a half-back whose scrum-half, Martin Roberts, showed the sort of zest that earned him international honours during November.
The Scarlets' problems lay up front where Ulster dominated the scrums in the absence of injured front-line props Kees Meeuws and Iestyn Thomas.
What's more, the visitors were able to take their chances while Nigel Davies' side simply ran out of options whenever a decent attacking option presented itself.
Ian Humphreys put Ulster into the lead with a 12th-minute drop-goal, but a 40-metre charge by home number eight David Lyons failed to produce a response as the move fizzled out.
Fly-half Jones levelled after 18 minutes with a penalty, but six minutes later Humphreys capitalised on poor defence, using his pace to make the line untouched.
Makeshift full-back Rhys Priestland - there due to Morgan Stoddart's injury absence - failed to field a high ball and the visitors were swift to capitalise.
Centre Darren Cave gave the final pass to midfield partner Paddy Wallace, who dived over after 32 minutes for Matt Williams' side to lead 13-3 at the break.
The Scarlets fight-back began from the first whistle after the break. They dominated territory and possession in the opening 15 minutes of the second half and were justifiably rewarded.
After centre Jon Davies was brought down a metre short on the right, the ball was returned along the back line for Daniel to cross on the other flank.
Stand-off Jones converted superbly with his right foot in the treacherous conditions and added a penalty to the 47th-minute try six minutes later with an equally well-struck penalty to level the scores at 13-13.
Humphreys responded with two failed long-range penalty attempts either side of a drop-goal effort that drifted wide.
However, the Ulster fly-half's boot continued to cause problems for the home defence, the pressure from his high kicks telling as it led to the 71st minute scrum at which the hosts were penalised.
Humphreys converted from a difficult angle, but opponent Jones replied two minutes from the end to level the scores for the final time.
Scarlets: Priestland, Daniel, King, Davies, M. Jones, S. Jones, Roberts, John, Rees, Manu, Cooper, Day, D. Jones, Easterby (capt), Lyons. Replacements: Williams for Daniel (56), Cattle for Roberts (75), Owen for Rees (61).
Not Used: Hopkins, MacLeod, Edwards, C Thomas.
Ulster: Cunningham, Trimble, Cave, Wallace, Danielli, Humphreys, Boss, J. Fitzpatrick, Best, Botha, O'Donoghue, Caldwell, Ferris, Pollock, Diack. Replacements: Steinmetz for Trimble (64), Schifcofske for Danielli (7), Court for J. Fitzpatrick (55), McCullough for Caldwell (58), Dawson for Pollock (64).
Not Used: Brady, Marshall.
Ref: R Poite (RFU).