Charlie Hodgson added eight points from two penalties and a conversion, although he missed a further three attempts on goal.
Another former England fly-half, Andy Goode, kicked two goals for the visitors.
Saracens were determined to set the pace of their first home game of the season and were ahead inside three minutes when Hodgson scored a penalty awarded for a breakdown offence.
Worcester struggled to get possession during the early stages as Saracens surprised their supporters by employing an expansive game despite the rain and greasy surface.
Worcester finally got ball in the 14th minute when referee Geraint Roberts penalised Saracens at a ruck. But Alex Grove turned over possession in a two-man tackle and the hosts won the scrum and resumed their offensive.
Miles Benjamin produced two big tackles to halt promising attacks and, for all their possession and territory, Saracens had to wait until the 20th minute for another scoring opportunity - but this time Hodgson's penalty crashed back off a post.
The price is usually high for such profligacy and, sure enough, Errie Claassens broke through, forcing a penalty out of the home defence. Goode equalised with a snap drop-goal to saving himself the job of kicking for goal off a tee.
The problem for the champions was that Worcester were playing very well without the ball, hustling and harrying ball-carriers, tactics which often paid dividends in the conditions.
And they also kept a close-eye on hooker Schalk Brits, so often Saracens' go-to player, although one challenge on the former Springbok was off the ball and left him requiring treatment.
Goode had a chance to give Worcester the lead three minutes before half-time, but his long-range penalty, while on target, faded in front of the posts.
Worcester finished the half pinning Saracens back inside their 22.
Kai Horsmann broke clear from a scrum on half-way, Saracens were forced to concede a lineout from his kick-ahead and then offended while defending close to their line.
Goode kicked the penalty, leaving their hosts looking bemused by a three-point half-time deficit.
Hodgson hauled his side level within two minutes of the re-start, drilling home a penalty after Worcester pulled down a maul.
Brits injured himself two minutes later, charging shoulder-first into an tackle. The hooker looked to have suffered concussion and was removed from the field by stretcher to be replaced by Jamie George.
Worcester had Saracens at full-stretch with an impressive succession of phases that saw the ball moved ever-closer to the line only for Goode to waste it all with a poorly-executed attempt at a drop-goal.
Just as bad was Hodgson's next kick at goal after Worcester failed to release in the tackle on 50th minutes. The former Lions and England fly-half hooked the ball badly wide of the far post.
But Saracens broke the deadlock three minutes later, and Hodgson sparked it.
His pass to Owen Farrell - who had just come on for Adam Powell - was whipped on to Strettle, who raced up the left wing and squeezed in by the flag despite the attempted tackle by Marcel Garvey. Hodgson's conversion attempt went wide.
Saracens struck again on the hour when Barritt raced onto a crash ball and battered his way over the line despite two defenders clinging onto the powerful centre. This time Hodgson converted.
Joe Carlisle, on for Andy Goode, tried to reduce the arrears with a penalty from 40 yards out, but it faded and dropped into the arms of full-back Alex Goode.
Garvey then broke clear of two tacklers on the right and kicked ahead only for a timely interception.
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