Welbeck was joined in the Arsenal starting line-up by defender Calum Chambers, with Theo Walcott, Jack Wilshere – who was making his return from an ankle injury - and Kieran Gibbs on the bench.
And it took just eight minutes for Welbeck to make an impact, stealing the ball from defender Papa Souare before the Palace man took him down for a penalty that Santi Cazorla tucked away.
He then claimed his second assist shortly before the break, firing in a shot that Julian Speroni could only parry into the path of Olivier Giroud for a goal that proved decisive.
Over in Wales, England international Jonjo Shelvey had a hand in the winner as Swansea came from behind to beat Manchester United 2-1.
Midfielder Shelvey's shot was deflected in off Bafetimbi Gomis to seal a league double for the Swans over United.
The Red Devils included several full Three Lions internationals within their side, with Phil Jones, Luke Shaw and Wayne Rooney all unable to stop them from slipping to a defeat.
Ben Mee scored a dramatic late equaliser as Burnley claimed a 1-1 draw at Stamford Bridge, the defender cancelling out Branislav Ivanovic's early strike.
Current U21 men Michael Keane and Danny Ings were in the Clarets starting eleven.
Elsewhere, another member of Gareth Southgate’s squad, Saido Berahino, could not make the breakthrough as West Brom took a point from the Stadium of Light after a goalless draw against Sunderland. Senior international Ben Foster was in goal for the Baggies.