Both wingers were handed starts at Bramall Lane and were involved in two goals each as the Gunners raced into a five-goal lead after just 39 minutes in a scintillating first-half display.
After Martin Odegaard slotted home Arsenal's opener in the fifth minute, Saka drove down the right flank and delivered a dangerous cross towards the back post that was diverted into his own net by Blades defender Jayden Bogle.
Martinelli then fired a deflected strike in at the near post on the 15-minute mark - Arsenal's 300th Premier League goal under Arteta - before assisting Kai Havertz to drill an accurate left-footed shot into the bottom corner before the half-hour mark.
Saka then registered his second assist of the night when he received the ball on the right channel inside the penalty box before picking out Declan Rice to coolly place a finish into the far corner.
After such a positive first 45 minutes for the Gunners, Saka was withdrawn at half time and replaced by Fabio Vieira, before Martinelli limped off with a foot injury midway through the second half, shortly after Ben White netted a superb sixth for the visitors.
Arteta has since delivered an update on both players, stating that Saka was feeling ill on the night, while Martinelli has sustained a cut to his right foot.
"[Saka] was feeling a bit sick. As well we have Fabio who we needed to give minutes," Arteta told Sky Sports in a post-match interview.
"We had a little issue with Gabi Martinelli. He had a little cut in his foot, so we need to see how it is."
On a positive note, midfielder Thomas Partey came on as a second-half substitute to make his first appearance for Arsenal since October 8 after a lengthy spell on the sidelines through injury.
"Today, obviously Thomas is available to play a certain amount of minutes. This was his first minutes after four months. Then like anybody he'll need to earn the right to play more minutes," said Arteta.
"I'm really happy with the players that played, really happy to get some players back after a long time, like Fabio [Vieira], like Thomas [Partey] and then maintain the momentum.
"Now [the focus is on] Brentford. We enjoy that today and tomorrow it's Brentford, Brentford, Brentford and keep going."
Arsenal, who have won all seven Premier League games since the turn of the year and have scored 31 goals in the process, remain third in the table despite their thumping win over Sheffield United, one point behind Manchester City in second and two behind leaders Liverpool.
Arteta will hope to have both Saka and Martinelli available for Saturday's home clash against the Bees, before Arsenal welcome Porto to the Emirates Stadium for the second leg of their Champions League last-16 tie three days later.