Gabriel, Gabriel Martinelli and captain Martin Odegaard all scored in the first half as the Gunners became the first team to win five consecutive away London derbies without conceding a single goal.
The Gunners began the day with second-placed Manchester City hot on their heels after a 1-0 win over Crystal Palace on Saturday pulled the reigning champs within two points.
With 11 games remaining, Mikel Arteta's side can stretch the gap to eight points with a home win against Crystal Palace next Sunday before Manchester City's next appointment in the Premier League.
"How does that sound? It's 11 finals for us, we take it game by game," said Leandro Trossard, who had a trio of assists as Arsenal took advantage of Fulham's porous defence at Craven Cottage.
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