Charlie Hodgson converted Samuela Vunisa's try and added two penalties to give Sarries a 13-3 lead at half-time, with Tom Catterick replying.
Hodgson then kicked two penalties after the break either side of Nick Tompkins' score from close range.
Fly-half Hodgson added a breakaway try late on before Billy Vunipola's score in added time sealed a bonus point.
Saracens remained the only unbeaten team in Europe this season and recorded their 13th consecutive victory over Newcastle Falcons in all competitions.
With new England head coach Eddie Jones in the crowd at Kingston Park, the north London side had to wait to be sure of victory as a kicking battle in the first half made for a scrappy game.
Newcastle, still without a league win this season, put pressure on Saracens' defence in the second half, but despite going through the phases they could not trouble the visitors' line.
It was from a Falcons attack that former England international Hodgson, who will retire at the end of this season, got the third try of the afternoon on 78 minutes after intercepting a loose pass and racing clear.
With the home side attempting to get on the scoreboard themselves in added time, a turnover and breakaway from Ben Ransom eventually allowed Vunipola to add Saracens' fourth score of the afternoon in the fourth minute of added time.
Newcastle director or rugby Dean Richards:
"I've not spoken to Eddie Jones, but I would have thought a lot of our guys should be in with a shout for England in the future, especially our hooker George McGuigan.
"It was 13-3 at half-time after we gifted them a try and, when it was 23-3, we started to push, made mistakes and conceded those two late tries.
"We started to chase the game and that fell right into their hands.
"They have a huge kicking game and they are very accurate in what they do. It enables them to sit back and wait and in the end their accuracy was far greater than ours."
Saracens director of rugby Mark McCall:
"It wasn't the most attractive of games.
"Newcastle came with a kicking plan and I was pleased with the patience and energy we showed.
"We stayed with it until the end and proved it's very important to be able to bring impact players like Billy [Vunipola] off the bench."
Newcastle: Tait; Agulla, Powell, Socino, Watson; Catterick, Young; Vickers, McGuigan, Welsh, Robinson, Green, Wilson, Welch (capt), Latu.
Replacements: Lawson, Rogers, Vea, Botha, Hogg, Takulua, Willis, Harris.
Saracens: Goode; Ellery, Tompkins, Taylor, Wyles; Hodgson, Spencer; Barrington, George (capt), Figallo, Itoje, Kruis, Wray, Fraser, Vunisa.
Replacements: Saunders, Vunipola, Du Plessis, Rhodes, Vunipola, De Kock, Streather, Ransom.
Referee: Andrew Small.
Attendance: 5,200.
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External overnight trips went up by 5%, reaching 2.3 million, due to a large influx of British people.
However, tourism numbers from the Republic of Ireland continue on a deep downward spiral.
In 2015 they slumped by 18% on the previous year, with the problem now being looked at by a "recovery task force" at Tourism Northern Ireland.
Overnight trips by visitors from across the border totalled 320,000 in 2015, while in 2012 there were 430,000 overnight trips made.
In 2014 a report for Stormont said an "image problem" may explain the fall, but the weakness of the Euro last year will not have helped.
The Department for the Economy's new statistics show that the Giant's Causeway remains the most popular visitor attraction.
In 2015 it had over 815,000 visitors.

Kent Police said the man, from West Sussex, sustained a serious injury when his Ford Focus came off the road in Hoath Way on Friday.
He was taken to Medway Maritime Hospital but died on Saturday evening.
Police said the car left the carriageway before mounting a grass verge and overturning. No other vehicles were involved.
It is not yet known why the man lost control of his car.
Saracens returned to the top of the Premiership table after securing a late bonus point in their win at Newcastle.
[NEXT_CONCEPT]
Visitor numbers to Northern Ireland hit an all-time high in 2015, according to new tourism statistics.
[NEXT_CONCEPT]
A 67-year-old driver has died in hospital after he crashed his car in Gillingham.