Brits' departure failed to knock Saracens off their stride, however, and despite playing with 14 men for 60 minutes after captain Brad Barritt had been sent to the sin-bin they were still able to cruise over the finishing line.
An otherwise uneventful first half was overshadowed by the red card shown to Brits, whose blows ended Wood's afternoon. Two seasons ago in the same fixture, Wood was sent off for stamping.
With Barritt having received a yellow card for a tip-tackle on Ross Moriaty, Brits' offence meant Saracens were forced to play 20 minutes of the first half with only 14 men.
That disadvantage did not present them from compiling a 13-6 interval lead, however, with Ransom's try seeing the reigning champions draw first blood.
Ransom chipped ahead as Saracens attacked from the 22 and the full-back gathered his own kick before touching down with Hodgson converting.
Two further penalties from Hodgson kept them in front, but with prop Rhys Gill limping off gingerly and Richard Wigglesworth departing the field while clutching his hand, their playing resources were depleting rapidly.
Gloucester were being pinned back in their own half and could only produce two penalties from James Hook, who also saw one promising break end when man of the match Will Fraser knocked the ball from his hands in the tackle.
Replacement prop Dan Murphy showed surprising pace as he surged into a gap, only for the supporting Hook to drop his pass as the try-line loomed.
Hook began the second half with a penalty but Saracens were soon back on to the front foot and after a spell of sustained pressure from a series of five-metre scrums, Hodgson was able to kick a penalty.
It set the tone for the remaining half hour as Hodgson found the target time and again in a forgettable afternoon for Gloucester.
