Walker scored all of his side's points for the third straight match
Saracens dropped their first points of the season as Worcester ended their eight-match Premiership winning streak.
The hosts battled to their second 12-12 draw in consecutive weeks after the same score at Sixways against Bath.
Fly-half Willie Walker kicked four penalties in four attempts for the Warriors, while Derick Hougaard also notched four for the visitors.
The draw extends Saracens' lead at the top of the table to seven points over nearest rivals Northampton.
Worcester led 9-3 at the break thanks to Walker's accurate boot, although it was not the best 40 minutes of Premiership rugby.
Unlike his opposite number, Saracens fly-half Hougaard missed a drop goal, plus two out of three penalties.
The nearest either side got to a try was just before the interval when Saracens pressed in the home 22.
The pressure told as Worcester fumbled the ball backwards and over their own line but were rescued when flanker Tom Wood just got to touch down ahead of visiting back row Andy Saull.
Referee Martin Fox penalised the home team for illegally holding onto the ball on the ground time and again after the break and Hougaard made no mistake each time as he turned a six-point deficit into a three-point advantage by the hour mark.
As the final 10 minutes arrived, Worcester were awarded another penalty when Saracens infringed at a scrum in their own 22 for Walker to continue his faultless display with a fourth kick, and the hosts held on for a battling draw.
Worcester rugby director Mike Ruddock:
"At 9-3 at half-time I thought we were going to press on and win the game if we played as accurately in the second half as we did in the first.
"Unfortunately, we were not quite as accurate and, for 20 minutes of the second half, we allowed Sarries to put us under pressure.
"They got a few penalties and nudged ahead so it was a good effort from our boys to come back against them because not many teams are doing that."
Saracens head coach Brendan Venter:
"I thought our team played really well. I don't think we have played that well and been 9-3 down at half-time before.
"There were so many opportunities out there for us to score tries but we have got two points and we keep going.
"I'm proud of the team. I'll tell them when I'm unhappy and tonight is not one of them."
Worcester: Latham; Garvey, Rasmussen, Tuitupou, Benjamin; Walker, Powell; C Black, Lutui, Taumoepeau, Rawlinson, Gillies, Wood, Sanderson, Horstmann. Replacements: Gear for Garvey (70), Arr for Powell (11), A Black for C Black (33), Fortey for Lutui (68), Sourgens for Taumoepeau (72), Kitchener for Gillies (68). Not Used: Collins, MacRae.
Saracens: Goode; Haughton, Ratuvou, Barritt, Wyles; Hougaard, Marshall; Gill, Brits, Nieto, Borthwick, Ryder, van Heerden, Saull, Joubert. Replacements: Penney for Wyles (31), Rauluni for Marshall (50), Skuse for Gill (50), Lealamanua for Nieto (50), Vyvyan for Ryder (50). Not Used: Reynecke, Barrell, Powell.
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