Saka showed great determination to win the ball ahead of Lewis Dunk and send Kai Havertz through to score the opening goal at the Emirates Stadium.
The Gunners took a narrow lead into the break before they were reduced to 10 men following Declan Rice's 49th-minute red card.
Brighton made full use of the numerical advantage to restore parity through Joao Pedro, who pounced on a rebound to score his second goal of the season.
While Arsenal may have been frustrated with the draw and the red card, Saka managed to achieve an impressive feat in the final match before the international break.
Saka replicates Henry feat
With his pass for Havertz's opener, Saka became the first Arsenal player to provide an assist in each of the first three matches of a Premier League since Henry in 2004-05.
Twenty years ago, Henry managed to register at least one assist in Arsenal's first three matches against Everton, Middlesbrough and Blackburn Rovers.
In fact, the Frenchman went on to provide three assists across the next two matches against Norwich City and Fulham to begin the 2004-05 season with assists in five consecutive matches.
While it remains to be seen whether Saka can continue his impressive run, he is currently sitting top of the assist chart alongside Chelsea's Cole Palmer.
Havertz ends wait for long-distance goal
Meanwhile, Havertz showed great composure to calmly lift the ball over Verbruggen from outside the box, with the strike representing the 34th goal of his Premier League career.
However, it was the first time the German scored from outside the box in his Premier League career, having failed to produce a long-range effort since his days as a Bayer Leverkusen player.
Unfortunately for Havertz, his strike could not fire Arsenal to victory as they Gunners failed to win a Premier League game they led at half time for the first time since April 2023.
Arteta's side can still take comfort from the fact they are unbeaten this season, and they will look to maintain that record in the North London derby against Tottenham Hotspur on September 15.