Neal is the first Oiler since Connor McDavid in February 2018 to score four goals in a game.
The four-goal outburst was the first against the Islanders since Patrik Elias scored four times for the New Jersey Devils in 2003.
Neal now has six goals in three games since being traded to the Oilers for underperforming Milan Lucic in the offseason. The six goals is just one less than Neal scored in 63 games last season with Calgary.
Lucic was still looking for his first point of the season with the Flames heading into Tuesday's contest against the Los Angeles Kings.
Neal won a silver medal with Canada at the 2009 World Championships and guided the expansion Vegas Golden Knights to the Stanley Cup finals two seasons ago.
Neal began and finished the sequence that ended with his first goal late in the first period.
He completed his hat trick with two power play goals, scoring from both sides of the Islanders' goal.
Neal scored his fourth goal from the front of the left faceoff circle 6:51 into the third.