The Gunners were behind after just 13 minutes when Bryan Mbeumo struck for Brentford before David Raya nearly gift-wrapped the hosts a second when he allowed Keane Lewis-Potter's shot to slip through his grasp .
Raya clawed the ball off his own line and one minute later Gabriel Jesus headed Arsenal back on level terms.
Mikel Merino then put the visitors ahead after 50 minutes before Gabriel Martinelli added a third with Ethan Nwaneri - the 17-year-old handed his first Premier League start in place of the injured Bukayo Saka - involved in both goals.
Gabriel Martinelli celebrates scoring Arsenal's third goal in their 3-1 triumph. (AP PHOTO)
The win took Arsenal six points behind Liverpool - while having played a game more - and ahead of Nottingham Forest, while Brentford remain in 12th.
Mikel Arteta's men will have the chance to reduce the gap to just three points when they travel to Brighton on Saturday, 24 hours ahead of Liverpool's big clash with Manchester United at Anfield.
Brentford, who'd won seven of their opening nine matches at home heading into the league's sole New Year's Day fixture, struck the first blow.
Martin Odegaard's pass was intercepted by Mikkel Damsgaard, who played in Mbeumo, with Riccardo Calafiori failing to put enough pressure on the Brentford forward.
Mbeumo was allowed to cut inside on his strongest foot before firing past Raya at his near post to take his goal tally for the season to 11.
After Arsenal just got away with Raya's clanger, they grabbed the equaliser when the Bees spurned multiple chances to clear their lines before Thomas Partey fizzed an effort from the edge of the area on Mark Flekken's goal.
The diving goalkeeper failed to divert the ball from danger and Jesus threw himself at the rebound to head home, landing his sixth goal in four appearances,.
Five minutes after halftime, Arsenal went ahead after Flekken made a mess of Nwaneri's corner and the ball fell to Jesus whose effort was blocked before Merino poked home. It was Arsenal's 25th goal from a corner since the start of last season.
Nwaneri, who became the youngest player in Premier League history at this ground two years ago, then cut in from the right flank before delivering an enticing ball into the Brentford box.
Nathan Collins headed the ball away from danger but his clearance fell only to Martinelli with the Brazilian's lethal finish flying past a flat-footed Flekken.
Nwaneri was substituted with 13 minutes remaining, but his performance will provide Arteta with hope he has found another solution to navigate Saka's two-month lay-off, and deliver the Gunners their first title in two decades.
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