The 19-year-old squandered a golden opportunity on the stroke of the break when he glanced a header wide, but made amends three minutes after the restart with a sweeping finish from Samir Nasri's pass.
Arsenal failed to score for the first time in 20 Premier League matches, although they did have the ball in the net twice, with Pierre-Emerick Aubameyang and Laurent Koscielny's efforts ruled out for offside against Sead Kolasinac.
Marko Arnautovic, reportedly a transfer target of an unnamed Chinese club, appeared to wave goodbye to the home fans as he was substituted in the second half, but this performance should give West Ham confidence about life after the Austrian.
Relive how the action unfolded in the capital derby courtesy of Sports Mole's minute-by-minute updates.
Subs: Adrian, Masuaku, Obiang, Snodgrass, Diangana, Perez, Carroll
Subs: Cech, Bellerin, Lichtsteiner, Monreal, Torreria, Ramsey, Nketiah
"West Ham bought Marko for peanuts," Danijel Arnautovic told talkSPORT this week. "They paid £20million for him, which is nothing in the current market. Now West Ham have a fantastic offer. It is close to double what they paid for him. "He wants to go to a new market and challenge for titles. This is what he wants. It is his great desire that West Ham accept the offer from China."