David Strettle bagged a double and Jamie George and Alex Goode also touched down with Saracens, Premiership leaders again, pulling away in the second half having gone in at the break 10-3 ahead.
Hodgson also contributed three penalties and two conversions for 18 points overall while Newcastle, previously unbeaten in two, had a solitary penalty from Phil Godman to show for their efforts.
Godman had a chance to put the first points on the board for Newcastle in the tenth minute following a penalty conceded by Saracens 15 metres out but his kick struck the left post.
The visitors earned another penalty three minutes later following an infringement by Saracens at the lineout and this time fly-half Godman made sure of his angles and put the Falcons on the board.
Saracens gave away their fourth penalty of the half less than a minute later on halfway, which resulted in Matt Stevens being sent to the sin bin.
Godman had the chance to extend the Falcons lead with Stevens in the bin in the 19th minute as Saracens were penalised on their own 22 but his kick drifted wide of the post.
The returning Hodgson missed a perfect opportunity to level the scores for Saracens as his penalty also fell victim to the strong crosswind.
Hodgson made up for the miss three minutes later with a try though, following Chris Wyles' elusive run down to the five metre line, and converted to put Saracens 7-3 ahead.
Falcons wing Ryan Shortland was penalised for a tackle on Will Fraser as both challenged for a high ball from Neil de Kock with Hodgson increasing Saracens' lead to seven going into half-time.
Hodgson was again on target from the tee at the start of the second half, converting a penalty from just inside the Newcastle half.
Saracens worked their set pieces well and Jackson Wray burrowed into the Newcastle half before knocking on at the 20-metre line.
From the resulting scrum though the Saracens forwards won a penalty which Hodgson converted to keep his fine return going.
And just before the hour the floodgates opened as Strettle chased down Goode's grubber, collecting one-handed as it bounced towards touch before grounding tightly in the corner.
The Sarries pack again showed their dominance five minutes later as they rolled over from a five-metre lineout, with George touching down for the try.
Goode continued the rout, scoring after a piercing run from replacement Duncan Taylor into the Newcastle 22 - the ball recycled out to the right touchline where he went in untouched.
And Strettle grabbed his second try of the game in the dying minutes - Goode converting after Hodgson had done the honours for his score.