Joel Tomkins marked his Saracens first team debut with two tries as a commanding second-half performance secured a fine win.
Rugby League convert Tomkins crossed twice after the break as Saracens, trailing for 55 minutes, took control as Nils Mordt kicked 16 points.
But Bath are running away with their pool, so this is one trophy the reigning Aviva Premiership champions will not be walking away with this season.
A Saracens XV combining World Cup-winning captain John Smit, Heineken Cup winning scrum-half Peter Stringer and a number of younger prospects filling in for the club's absent England and Wales players, struggled to click in the early stages.
Worcester had the first scoring opportunity with a third-minute penalty, but Joe Carlisle's kick rebounded off the far post.
Worcester struck less than a minute later when two drives caught Saracens loose in their 22, and blindside Sam Betty emerged behind the home defence and dived over, Carlisle adding the conversion.
Stringer was twice involved as Saracens launched their first serious raid and the visitors were forced to offend on their line to prevent a try. Mordt successfully kicked the penalty.
The South African fly-half struck again five minutes later as another Saracens attack was halted by offside offenders, and Mordt's close-range goal reduced the deficit to one point.
But Tom Arscott quickly increased the gap again after 16 minutes, cleverly gathering a ball bouncing up the right wing while racing ahead and holding off Michael Tagicakibau to score behind the posts. Carlisle again added the conversion.
Tomkins looked eager for work on his first-team debut, but most of his early duties concerned defence and support as the centre saw little ball during the opening quarter.
Saracens scored a try straight off the training ground in the 25th minute. Mordt kicked a penalty to touch, Jamie George's throw to the back was caught and thrown down by Eoin Sherriff and from the drive, Stringer smuggled the ball from the back and sped over at an angle.
Mordt kicked the extra points to get Saracens back to within a point.
While no classic, the game continued to ebb and flow in the second half, both teams seeking openings to exploit and both defences determined to defy.
Mordt had a chance to edge Saracens into the lead for the first time after 55 minutes when Worcester were caught offside but his penalty was poor.
Yet Saracens won the restart and pressed on the left until the visitors cracked.
Stringer's pass sent James Cleverly driving for the line, and when he was stopped the ball reached Justin Melck who grounded the score. Mordt kicked the conversion.
The crowd reserved their biggest cheer for the third try on 61 minutes.
Tomkins read a Worcester attack well enough to intercept a pass from Danny Gray and sped clear of the cover the score between the posts, Mordt again converting.
Before the roars died down, Jackson Wray linked superbly with Tomkins on the left, sending the debutant haring in for his second try in the 65th minute, and Mordt's conversion edged in off the near upright.
Jamie George touched down with four minutes remaining as the turnaround was completed.
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