Fly-half Glen Jackson kicked 22 points and created a try as Saracens eased into the semi-finals of the European Challenge Cup.
Tries from Samoan international prop Cencus Johnston and young South African centre Brad Barritt in a five-minute spell in the first half effectively killed off Newcastle's challenge.
Jackson's haul consisted of five penalties, two conversions and a drop goal and he constantly pegged the visitors back with his accurate tactical kicking.
Saracens will visit Northampton, who beat Connacht 42-13 in their quarter-final 24 hours earlier, on May 2 or 3.
Newcastle, who arrived at Vicarage Road desperate to avenge their 44-14 Guinness Premiership hammering by Saracens last September, soon had their hopes dashed.
The Falcons opened the scoring with ninth-minute penalty from fly-half Tom May but that was all they had to show for a promising opening in which former All Blacks prop Carl Hayman was prominent.
By the time former rugby league winger Danny Williams scored their first try in the second half they were already a well-beaten team,
but their perseverance resulted in a try for skipper Phil Dowson in the dying seconds.
Saracens responded to May's early penalty with close-range penalties from Jackson in the 17th and 24th minutes before scoring the vital tries.
A penalty from Jackson found touch deep in the Falcons half and Saracens won the resulting lineout before their third forward drive took Johnston over.
Jackson added the conversion and also added the points five minutes later after setting up his side's second try for Barritt.
The fly-half threaded a short kick through the Newcastle defence and the 22-year-old Springbok timed his run perfectly to snatch up the ball and dive over.
Jackson stroked over a 40-metre drop goal to increase Saracens lead to 23-3 a minute before half-time.
Newcastle tried to hit back with prop David Wilson and full-back Alex Tait involved in the build up which released Jamie Noon and only Sarries scrum-half Neil de Kock's ankle-tap tackle denied the England centre a try.
Saracens, under intense pressure, conceded two penalties near their own line, but the visitors were repelled after twice opting to attack the line.
Saracens should have had a third try after Jackson swerved clear on a 50-metre dash out of defence and found Rod Penney but the winger looked for support instead of going for the line.
Jackson increased the lead to 26-3 with his third penalty in the 53rd minute but Newcastle finally hit back five minutes later.
Tonga-born centre Tane Tu'ipulotu was stopped just short of the home line but, with Saracens committing numbers to halt the resulting forward assault, he lofted an excellent kick towards the left corner for Williams to collect and touch down in the 58th minute.
But Saracens rounded off victory with two more penalties from Jackson before Newcastle flanker Dowson crossed for his late consolation try.