The win pulls Sarries into 10th position on the Premiership table, getting ahead of the Leeds Tykes on points difference.
The Falcons will find this latest defeat hard to swallow – this is the eighth time this season that they have lost a match by less than a score.
Sarries Winger Richard Haughton – fresh from England Sevens duty in Los Angeles – scored a brace of tries for the home side, whilst former All Black skipper Taine Randell and flanker Ryan Peacey also touched down.
But it was the fine performance from Castaignède that caught the eye, with the French star pulling the strings from fly-half – producing dazzling breaks to create tries out of nothing for both Haughton and Randell.
Haughton also set up a score for Peacey before racing away with an interception for his second of the game to kill off the Falcons.
Warren Britz, Phil Dowson, Dave Walder and Joe Shaw went over for the visitors, but it was not enough to stem the Castaignède show – the Frenchman added three conversions and a penalty to make the all-important difference.
For Saracens:Tries: Haughton 2, Peacey, RandellCons: Castaignède 3Pens: Castaignède, Kydd
For Newcastle Falcons:Tries: Britz, Dowson, Walder, J ShawCons: Walder 2Pen: Walder