The visitors hit back from 12-0 down with tries from Thomas Castaignede, Ben Russell and Ben Johnston in front of their new signing Andy Farrell.
Before that, Worcester got off to a flyer when Ben Hinshelwood's double try burst inside the first 16 minutes gave them a great platform.
Both sides opened up with ambition, throwing the ball wide at every opportunity.
Worcester began to find their way and strong runs from Dale Rasmussen and Giscard Pieters served notice of their power in the backs.
With fly-half James Brown, making his first appearance since an appendectomy, pulling the strings the Warriors were making sure Saracens were pinned back in their own 22.
After five phases of slick rugby, Worcester opened the scoring with Hinshelwood powering his way to the line following a great offload by Rasmussen. Brown missed the conversion but the Sixways side were definitely in charge.
It just got better for the Warriors on 16 minutes when after, more power play, Scottish international Hinshelwood's chip and chase was too good for Dan Scarbrough and Worcester, once Brown added the extra points, were 12 points to the good.
The visitors always looked dangerous, especially with Castaignede showing his tricks.
The Frenchman shimmied his way to the line midway through the half to begin the comeback.
Nicky Little slotted the conversion but Saracens found themselves up against it with six minutes of the half left when Iain Fullarton was sin-binned for a punch.
Brown extended Worcester's advantage with a late penalty but Saracens hit back in stoppage time with a Russell try and a Little conversion following more Castaignede magic.
Saracens came out fighting in the second period and, after dominating the opening exchanges, wing Johnston found enough space to speed in on the left and the visitors were ahead for the first time in the match.
They continued to force the pace with Worcester hanging on during most of the half but, crucially, the Warriors kept the score to within four points.
Hinshelwood was once again involved in the best Worcester attacks but Saracens dominated possession and their defence was frustrating the home crowd.
Their drive was also impressive and, after winning line-out ball with six minutes left, Castaignede had the perfect opportunity to put the game to bed.
His penalty sailed wide and, following a late Little knock-on, Worcester had one last chance to snatch victory.
After a couple of phases, they won a penalty and Brown brought the deficit back to a point but they just ran out of time to complete the recovery.
The losing bonus point was enough to lift Worcester up to ninth in the table before London Irish's clash with Gloucester.
For Worcester Warriors:Tries: Hinshelwood 2Con: BrownPens: Brown 2
For Saracens:Tries: Castaignede, Russell, JohnstonCons: Little 2