Fly-half Lozowski, a replacement for injured England fly-half Owen Farrell, looked nervous at first, missing a sitter of a penalty.
It was his boot, however, that gave the hosts a 6-3 interval lead. Worcester’s solitary riposte was a Ryan Lamb penalty in quite a poor opening period that just about resembled a contest.
England brothers Billy and Mako Vunipola were constant thorns in the side of the Worcester midfield but the visitors held their ground and had their own chances to score.
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New signing Ben Te’o, the rugby league convert who went on tour with England to Australia this summer, drove into the Saracens 22 and looked set to go over before Alex Goode pulled him to ground.
The closest either side went to a try in the first half came when England lock George Kruis was just short of the line before Lozowski found the target for a second time on the stroke of the interval.
After that it was all one-way for Sarries, and Lozowski also grew in confidence as he scored a try and booted two more penalties and another two conversions. Hooker Jamie George, on his 150th appearance, South African back row Shalk Burger, in his first game for the champions, also went over.
Saracens had to wait before they secured their bonus point.
It came in the 77th minute but it was worth hanging on for - all thanks to a brilliant, side-stepping solo score from replacement scrum-half Ben Spencer that had Saracens fans in raptures. Saracens are aiming to become the first team to win three successive domestic crowns since 2005. But, despite the scoreline, they will know they never really got up to the free-flowing rugby of the past.
Lozowski’s 20 points was six more than he accumulated for Wasps last season!
SARACENS: Tries George, Lozowski, Burger, Spencer. Cons Lozowski (3). Pens Lozowski (3).
WORCESTER: Pens Lamb (1)