Hodgson scored one of five tries - Joel Tomkins, Owen Farrell, Chris Ashton and Alex Goode claimed the others - and booted four penalties and four conversions as Edinburgh were completely outclassed.
Saracens were on top right from the start and former rugby league star Tomkins marked his Heineken Cup debut by claiming the opening try when Edinburgh were caught out by a quick tap-penalty move in the 16th minute.
Hodgson's immaculate form with the boot carved out a 16-0 half-time lead for the visitors.
The home side's cause was hardly helped when they lost skipper Craig Laidlaw and leading scorer Tim Visser to injuries at the break.
Scrum-half Richie Rees threatened with a powerful run from deep in his own half but was brought down 10 metres short of the Sarries line. Schalk Brits was handed a spell in the sin bin for not releasing Rees after he had been tackled.
But Sarries coped comfortably with being a man down and Hodgson thumped over a long-range penalty to extend their lead.
Farrell had only just been entered the action when he stormed over in the corner for a second Sarries try just before the hour mark.
Edinburgh were looking a well beaten side know and Ashton underlined the visitors' superiority as the held off a couple of weak tackling attempts to dive over near the posts for a third try.
Goode provided the finishing touch to a flowing move to claim a fourth score and secure a bonus point.
Hodgson then capped his impressive performance with a trademark charge-down try, pouncing on Harry Leonard's attempted clearing kick and strolling over for Sarries' fifth and final score.
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