The visitors could have pulled off an unmerited win if Nils Mordt and Sam Stanley had not missed with four routine penalties.
In a game of stout defence, neither side showed enough attacking nous to threaten the tryline but the home pack were the dominant force, which enabled Andy Goode to kick them to victory with three penalties and a drop goal.
Saracens were minus at least eight of their first choice line-out due mainly to international commitments. In contrast, Worcester were only without Samoan captain David Lemi.
The Warriors had the better of the first 10 minutes and were rewarded with the first score when Goode kicked a 30-metre penalty.
Moments later, the visitors had their first chance for points but Mordt was off target with his 45m penalty attempt.
Worcester suffered a blow when young centre Joe Carlisle hobbled off in the 14th minute, to be replaced by Alex Grove.
The Warriors suffered another setback when Mordt brought the scores level with a simple penalty.
Then at a ruck 45m out, Saracens were penalised but Goode could not take advantage and the score remained at 3-3 at the end of the first quarter.
Worcester were denied the first try of the game when, close to the Saracens line, Errie Claassens somehow failed to gather a clever chip ahead from Goode.
However, the hosts were not to be denied points for long as Goode put them back in front with his second penalty.
The outside half then missed a 35m drop goal attempt before Saracens lost flanker Jackson Wray to a leg injury.
A poor clearance from Goode allowed Ben Ransom and Duncan Taylor to counter-attack and when the Warriors were penalised for offside, Mordt had a good chance to tie the scores - but his 35m kick was a poor one.
Worcester extended their lead when a Ransom kick was charged down to put his side under pressure.
Warriors won a ruck close to the visitors' line and Goode fired over a drop goal from point blank range, before the outside half added a penalty to give Worcester a deserved 12-3 interval lead.
The first 10 minutes of the second half represented the best period of the match for Saracens. The visitors dominated in terms of possession and territory but they were not able to convert it into points as James Percival and Josh Matavesi both stole crucial ball from them at vital stages to relieve the pressure.
After 51 minutes Mordt was presented with another penalty chance but once again he failed as his 30m kick rebounded back off a post.
It could have been worse for Saracens but Goode failed with both a drop goal and a long range penalty.
It therefore remained at 12-3 going into the final quarter and just afterwards the unhappy Mordt was withdrawn.
Sam Stanley was his replacement but he fared no better on the kicking front, with a 30m penalty miss depriving his side of a bonus point.
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