Under pressure from Exeter Chiefs to claim top spot again, Saracens coped impressively throughout the game to claim a sixth successive win as Newcastle's wait for a victory continued.
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An early penalty allowed Saracens to find the first score of the game as they kicked for touch, before a driving maul resulted in Samuela Vunisa claiming the try on his full debut.
Much of the first half was spent with the two sides kicking into the air as both teams found it difficult to enjoy superiority.
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Hodgson held his nerve to extend the lead to 13-3 just before the break and another penalty early in the second half handed the visitors a cushion as Newcastle struggled to find any rhythm.
Any doubts about the result were put to bed with 15 minutes remaining as Newcastle held up Jamie George on the line, before failing to prevent Nick Tompkins from diving over for the second try of the afternoon.
Hodgson sent over another penalty, and there was still time for Saracens to add two more tries try late on as the former England fly-half intercepted a pass before sprinting clear but he was unable to follow the piece of brilliance with a conversion as he settled for a tally of 21 points.
Neither Newcastle or Saracens were keen to finish the meeting as the game ticked into extra time, and it was Billy Vunipola who battled his way over the line to secure the bonus point before Andy Goode ended the contest with the conversion.