Saka opened the scoring early on before Kieran Tierney added another goal just before the break. The England forward got his brace midway through the second half, while Alexandre Lacazette, with a penalty, and Emile Smith Rowe wrapped up the victory.
The win takes Arsenal to 35 points from 19 games following their fourth straight league victory, just over two years since manager Mikel Arteta’s first match in charge of the Gunners.
They have a six-point lead over fifth-placed Tottenham Hotspur, although their London rivals have three games in hand.
The visitors took the lead after six minutes through Saka, who stroked the ball past goalkeeper Angus Gunn, who was making his Premier League debut, following a neat passing move that led to Martin Odegaard laying the ball into the forward’s path.
Arsenal continued to test the Norwich defence with Saka the danger man thanks to his jinking runs down the wing and Gabriel Martinelli also posing a threat as the Gunners dominated.
Norwich’s last top-flight Boxing Day win was in 1987 so the signs were ominous for the struggling Canaries from the start.
However, it took Arsenal until just before halftime to score again on the break when Scotland left back Tierney fired home a low shot, with Odegaard again providing the killer pass.
Norwich stayed in the game until the 67th minute but then the floodgates opened as the visitors struck three times.
England forward Saka got Arsenal’s third goal with another precise strike after cleverly weaving his way past Brandon Williams on the right edge of the area.
Lacazette was then fouled in the box by Ozan Kabak, and the Frenchman got up to convert the spot kick in the 84th.
Substitute Smith Rowe complete the rout with a goal in added time, leaving Norwich on 10 points – three adrift of fourth-bottom Watford having played two games more.