Saracens were already 22 points clear when Farrell joined the action, but he set up his team's fifth and final try by securing line-out possession before fellow substitute Shane Byrne scored in the corner.
Farrell took his place in the Saracens back row and his next taste of action could be next Friday night's appointment with Premiership champions Sale Sharks in Stockport.
Farrell followed up his union debut in a Guinness A League game last Monday by displaying some solid touches as Saracens took maximum advantage against a Newcastle side that offered little resistance in the forward battle.
Farrell spent some 18 months fighting to overcome a succession of injuries but he now has a full season ahead of him after his six-figure cross-code switch.
"It has been a long time coming, so it was nice to get out there and get this game under my belt," he said.
"I was eager to get on, and as the clock wound down, I wasn't sure if it would happen.
"The boys already had the game under control, so that made it a pretty easy debut for me but the most important thing was that we won the game.
"I have put all thoughts of my injuries behind me. I just wanted to get out there and play some rugby, and now that I have done that, I can move on to better things."
Saracens rugby director Alan Gaffney expressed satisfaction at Farrell's Premiership entry, adding: "I thought Andy was fine in the 16 or so minutes he was on the pitch.
"He got a fair bit of a legal 'shoeing', which I thought was good for him. He has got a grin on his face.
"His fitness level would be reasonable for most people in the Premiership but not at the level Andy Farrell himself would want to be at."
Gaffney said he would weigh up his selection options regarding Farrell over the next couple of days, but it would appear he could again be on the bench at Sale, while Saracens also have two A games scheduled for next week.
By the time Farrell arrived, Saracens were home and dry courtesy of a superbly controlled display by their pack.
Byrne and his fellow forwards Matt Cairns, Kevin Yates and Ben Russell all scored tries to emphasise Saracens' dominance up front, while centre Kevin Sorrell marked his 150th Premiership appearance by also breaching Newcastle's defence and fly-half Glen Jackson kicked 19 points.
"It was a huge step forward for us," said Gaffney. "I thought we showed a lot more composure today and, the forwards have certainly worked very hard. They can be delighted with what they did."
Newcastle look to have a long and difficult season ahead of them as once again they were found out when it came to critical forward areas.
They were dismantled at times by the Saracens scrum and a 30-metre rolling maul try provided the defining image of the game as Newcastle's pack found themselves in a crumbled heap under their own crossbar.
Despite the absence of knee-injury victim Jonny Wilkinson, they offered some neat touches behind the scrum as Jamie Noon, James Grindal and 6ft 4ins wing Tim Visser scored tries, but Saracens were never seriously threatened.
"I thought the key moment was losing Mike McCarthy to the sinbin right at the start of the second half," said Falcons rugby director John Fletcher.
"We had talked about keeping 15 players on the pitch, but we didn't get that and Saracens scored a couple of tries.
"Their pack played well today, and we know we have got to improve quickly in some areas, but we have got to take this on the chin, work hard and work smart because we have only got five days before our next game against London Irish."