And Mark McCall's side extended their lead through Ben Spencer's angled penalty, before the Aviva Premiership champions continued to pile on the pressure with Bristol conceding penalties and territory regularly.
Bristol's defence did well to hold firm with Jordan Crane and Will Cliff combining well to clear their lines, although Brad Barritt came within inches of extending his side's lead as he was held up inches short.
Saracens were still asking the questions, and after winning a scrum against the head Mike Ellery surged forward down the right flank - but his offload was adjudged to be forward by referee Ian Tempest and the score stayed at 10-0 until half-time.
A fine long-range penalty from Spencer just after the interval was ominous for Saracens, and another heroic effort from Lozowski saw him rewarded with his second try of the night as he charged down a Bristol clearance.
Spencer made no mistake with the conversion, and the visitors were in control at 20-0.
Andy Robinson's side missed out on a golden opportunity on the Saracens five-metre line as first Maro Itoje rose highest to steal their lineout, before Bristol won the ball back only for the Saracens' scrum to hold firm.
And McCall's side made them pay as great hands from forwards Schalk Burger and Jackson Wray released Wyles to score in the left corner just before the hour mark, as Lozowski added to his tally with a touchline conversion.
Bristol were so unlucky not to score in the 66th minute as both Williams and Jack Wallace came close in quick succession after Saracens were caught offside.
But Saracens smelled blood when Max Crumpton was sent to the sin-bin for maul infringement, and on 72 minutes George powered over from close range at the back of a maul to secure the try bonus point.
George Perkins showed supreme pace to dot down but the TMO ruled out his effort on the grounding, although Saracens were not done just yet as Kruis reached over to touch down on his return from injury and put even more gloss on the scoreline.