The result at Vicarage Road moved Saracens back into second place in the table.
Hodgson, returning to the side after four weeks out with a fractured cheekbone, landed seven penalties and a conversion - with only one miss - to hand captain Steve Borthwick victory on his 100th appearance for the club.
But they were pushed all the way by Gloucester who competed superbly but were ultimately sunk by replacement Richard Wigglesworth's crucial second-half try for Sarries.
Gloucester, who had two players sin-binned, replied with tries from prop Dan Murphy and flanker Akapusi Qera, with Billy Twelvetrees kicking their other 13 points.
Twelvetrees, switched from centre to fly-half with Freddie Burns on England duty as a replacement in the Twickenham triumph over New Zealand, kicked Gloucester into an early 6-0 lead with penalties in the second and seventh minutes.
Hodgson's second penalty levelled the scores at 6-6 in the 27th minute but, two minutes later, Gloucester scored the first try of the match after the former England fly-half's clearance kick was charged down.
Prop Murphy, who blocked the kick, produced a neat touch to control the ball with his boot and a clean pair of hands to collect it and drive over the line, with Twelvetrees converting.
But, three minutes later, Murphy became the villain when he was sin-binned by referee Sean Davey for killing the ball at a ruck. Hodgson made partial amends for his earlier blunder by kicking the resulting penalty.
Gloucester sent on Nick Wood as a temporary front-row replacement for Murphy but his first scrum was penalised on the halfway line and Hodgson made his fourth kick appear effortless from the halfway line to reduce the deficit to a single point four minutes before the interval.
Hodgson struck again to kick Saracens ahead three minutes into the second half after Gloucester were penalised for failing to roll away at the tackle.
But Gloucester responded with number eight Sione Kalamafoni making a surging run through the middle from the halfway line before their pack mounted a concerted series of forward drives.
They moved the ball wide before Qera crashed over in the left corner, with Twelvetrees adding the conversion from the touchline.
Saracens, stung into action, came storming back and when Kalamafoni blatantly killed the ball at a ruck he became the second visiting player to be yellow-carded.
Gloucester were forced to defend desperately as Sarries, attempting to capitalise on their second extra-man advantage, threw everything at them in a series of forward assaults.
Gloucester somehow kept them out but they were conceding penalties and Hodgson landed his sixth in the 54th minute before suffering his first miss at the seventh attempt three minutes later as he tried to kick the home side ahead from long range.
But Saracens took the lead for the second time in the match when full-back Chris Wyles, back from international duty with the United States, split the Gloucester defence before releasing replacement scrum-half Wigglesworth who crossed in the corner for a real winger's try, converted by Hodgson.
Twelvetrees cut the gap to two points with his third penalty before Hodgson responded with his seventh.
Gloucester mounted a desperate late assault which saw Wigglesworth sin-binned but Saracens managed to soak up the pressure.
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