But they were made to work for it by a spirited Treviso side, who remained in contention until the final 20 minutes.
Brendan Williams got the scoring under way with an early try, while Dion Kingi was Treviso's other try scorer.
But Vyvyan's tries either side of half-time, doubled with Jackson's accurate kicking, put Saracens clear.
Saracens director of rugby Steve Diamond:
"This is a hard place to leave with a victory, and you have to be happy with that result. Their players had a lot of passion and it was a tough game.
"We played in the right areas of the field, and you have to say we should have scored the bonus point - especially when you look at how much possession and how many chances we had.
"I thought it was another very good performance from Glen Jackson. He's beginning to show the sort of form we knew he had when we signed him.
"He was helped by our pack, though - they were dominant and gave Glen plenty of time to run the game. Our forwards are playing well and Glen's enjoying the ride at the moment."
Treviso: Williams; Perziano, Legg, Barbini, Calanchini; Smith, Troncon; Faliva, Ongaro, Costanzo; E. Pavanello, Wentzel; Garozzo, Orlando, Kingi.
Replacements: D. Dallan for Perziano (75), Picone for Troncon (66), Mazino for Faliva (56),
Tejeda for Ongaro (70), A. Pavanello for E. Pavanello (70), Dal Maso for Orlando (56).
Not Used: Palmer.
Sin Bin: Kingi (31), Tejeda (70).
Saracens: Castaignede; Bailey, Sorrell, Johnston, Scarbrough; Jackson, Dickens; Yates, Byrne, Visagie; Raiwalui, Fullarton; Vyvyan, Randell, Skirving.
Replacements: B. Russell for Johnston (19), Raulini for Dickens (75), Cairns for Byrne (60), Chesney for Fullarton (49), Seymour for Randell (51), B. Russell for Skirving (71).
Not Used: Broster.
Ref: D Changleng (Gala).