The visitors trailed 28-7 at the interval despite getting off to the dream start, with a try inside the first two minutes.
Oscar Usher hit a crash ball line to score in the right corner after a line-break from Alex Hearle and support from Elliott Obatoyinbo, with Brett Connon nailing the touchline conversion.
They were only denied a second try when the TMO deemed Tom Christie to have had a toe dead in goal following a Freddie Lockwood surge down the left, but Sarries drew level when Simón Benítez Cruz was sin-binned for a deliberate knock-on near his own line – referee Joe James awarding the hosts a penalty try.
They made the extra man count on 15 minutes when Rotimi Segun struck from turnover ball, chipping and chasing for a converted try down the left wing.
A jackal turnover from Tom Christie prevented further gains as the Kiwi snuffed out a Saracens attack near his own try-line, but it was only a temporary reprieve as Noah Caluori chased down a grubber to the right corner for a converted score on 25 minutes.
Andy Onyeama-Christie had a try chalked off by the TMO for a knock-on in the build-up as the Londoners chased their four-try bonus point, but they did not have long to wait as Caluori dived in at the right corner less than a minute later.
That gave Sarries a 28-7 half-time lead, and they added to their tally shortly after the resumption when Onyeama-Christie collected an offload from Tom Willis to scamper over for their fifth converted try.
Caluori completed his hat-trick two minutes later when a quickly-tapped penalty was worked along the line for a score in the right corner, and it got worse for the Red Bulls when replacement hooker James Hadfield was driven over from a catch-and-drive down the left.
The Red Bulls offered some signs of resistance when fast feet from Obatoyinbo and a line-break from Ethan Grayson got them in behind the defensive line, but the attempted inside pass went to ground in a passage which summed up Newcastle’s frustrations.
Saracens responded with a pick-and-go try from Eroni Mawi on the hour mark, with Hadfield repeating the trick four minutes later.
Newcastle, to their credit, kept going until the end, but had to finish the game with 14 men when Christian Wade limped off with all his side’s replacements already used.
There was still time for two more Sarries try, however, with Caluori latching onto a Tompkins grubber to score in the right corner, followed in the last minute by Tompkins himself from a close-range penalty.
The Red Bulls at least had the final say on a difficult afternoon, Reuben Parsons marking his PREM debut with a try down the left from the very last play.
Saracens: 15 Elliot Daly (Max Malins, 50), 14 Noah Caluori, 13 Alex Lozowski, 12 Nick Tompkins, 11 Rotimi Segun, 10 Owen Farrell (c), 9 Charlie Bracken (Ivan van Zyl, 68); 1 Rhys Carre (Eroni Mawi, 50), 2 Jamie George (James Hadfield, 50), 3 Tietie Tuimauga (Harvey Beeton, 50), 4 Nick Isiekwe, 5 Hugh Tizard (Harry Wilson, 54), 6 Juan Martin Gonzalez, 7 Andy Onyeama-Christie, 8 Tom Willis (Nathan Michelow, 62).
Scorers - Tries: Penalty try, Rotimi Segun, Noah Caluori 4, Andy Onyeama-Christie, Eroni Mawi, James Hadfield 2, Nick Tompkins. Conversions: Owen Farrell 7.
Newcastle Red Bulls: 15 Ethan Grayson, 14 Christian Wade, 13 Alex Hearle, 12 Sammy Arnold (Cameron Hutchison, 65), 11 Elliott Obatoyinbo (Oli Spencer, 65), 10 Brett Connon, 9 Simón Benítez Cruz (James Elliott, 59); 1 Murray McCallum (Adam Brocklebank, 47), 2 George McGuigan (captain, Ollie Fletcher, 54), 3 Richard Palframan (Luan de Bruin, 56), 4 Oscar Usher (Finn Baker, 69), 5 Jamie Hodgson, 6 Tom Gordon (Reuben Parsons, 54), 7 Tom Christie, 8 Freddie Lockwood.
Scorers - Tries: Oscar Usher, Reuben Parsons. Conversions: Brett Connon 2.
Referee: Joe James. Attendance: 8,544.