[First scorer....Bredtner]
The Gunners lacked a killer touch during a frustrating first half but were grateful to go into the break on level terms after giving away a penalty.
Obafemi Martins stepped up to the spot only to see his poor effort easily saved by Manuel Almunia with 25 minutes on the clock.
Arsene Wenger's men came out fired up for the second half and Nicklas Bendtner broke the deadlock after 57 minutes.
Martins made amends for his penalty miss just 60 seconds later to pull Newcastle level.
But the Toon faithful were quickly silenced when Abou Diaby restored the lead after 64 minutes.
And Samir Nasri wrapped up the points for the Gunners just three minutes later — pushing Newcastle back into the bottom three on goal difference.
Despite the scoreline, Wenger admitted his side had endured a tough 90 minutes.
The Frenchman said: “We suffered a bit in the first half under the pressure.
"In the second half we took over, created many chances and deserved to win."
Striker Robin van Persie claimed the second-half performance was a sign of Arsenal's resilience.
He said: “We didn’t start that well. Newcastle were sharper, better, they wanted it more.
“When we scored we thought we could take it easy a little bit but that wasn’t the case because Martins scored within a minute.
"After that we knew we had to crack on and at least score one more goal."
The win completes a good week for Arsenal after they came back from a goal down against Hull in midweek to progress to the FA Cup semi-finals.
And Van Persie believes the Gunners can take a lot of confidence from the results.
He added: “It tells us that we can bounce back. We showed it against Hull last week and we showed it again today.
“I think this team has a lot of character and it’s up to us to show it until the end of the season because we can win lots of things this year.”
Newcastle: Harper, Steven Taylor (Owen 65), Coloccini, Bassong (Beye 38), Jose Enrique, Ryan Taylor, Butt, Nolan, Duff, Lovenkrands (Ameobi 79), Martins. Subs not used: Krul, Smith, Gutierrez, Geremi.
Goal: Martins 58.
Arsenal: Almunia, Sagna, Gallas, Toure, Clichy, Arshavin (Song Billong 74), Denilson, Diaby, Nasri, Van Persie, Bendtner (Eboue 89). Subs not used: Fabianski, Eduardo, Vela, Djourou, Gibbs. Booked: Gallas.
Goals: Bendtner 57, Diaby 64, Nasri 67.
