The Gunners were put ahead thanks to a Nicklas Bendtner header on 57 minutes, before Obafemi Martins levelled for Newcastle one minute later.
In the 64th minute Abou Diaby restored Arsenal's lead before Samir Nasri hit a third on 67 minutes.
The Geordies had a chance to open the score line in the first half when Peter Lovenkrands was brought down in the area by Manuel Almunia.
However, the Spanish keeper made up for his mistake by catching Martin's weak penalty-kick.
In the second half, Bendtner did well to head Andrei Arshavin's free-kick past Steven Harper.
Moments later, Martins capitalized on William Gallas' misjudgement to slot home for Newcastle.
A lovely exchange of passes between Robin van Persie and Diaby allowed the latter to go through on Harper and score Arsenal's second.
Nasri wrapped up the win for Arsene Wenger's men with after shooting from tight angle.