The pair left it late with their strikes coming in the last seven minutes.
Arsene Wenger placed his faith in youth in last season's Carling Cup and the young Gunners were narrowly edged out by a full-strength Chelsea in the final at the Millennium Stadium last February.
Sam Allardyce, just like former Chelsea boss Jose Mourhino, opted to place his faith in the tried and tested.
Newcastle looked stronger on paper, but there was little to separate the two sides in the early exchanges.
Obafemi Martins was denied by a smart save by debutant keeper Lukasz Fabianski ten minutes in.
Bendtner should have done better on 17 minutes when he met an inviting cross from Armand Traore, but the tall Dane didn't get over the ball and headed high over the bar from close range.
An Emmanuel Eboue cross from the right on 25 minutes took a deflection that almost re-directed the ball into the net as the Gunners looked to be taking control .
Newcastle did venture forward on occasions and Martins should have at least tested the keeper on the half hour when he got goal-side of Philippe Senderos.
The defender lost his balance and the Newcastle striker had just Fabianski to beat but instead blazed his shot high and wide.
Eboue tested Shay Given on 38 minutes with a well-struck low drive that the Irish keeper just about got a hand to prevent the ball finishing in the bottom right corner of the net.
Arsenal began the second half the way they ended the first. Given had to be at his best on 52 minutes to palm away yet another Eboue drive and with seconds he was fending off a powerfully struck drive from Theo Walcott.
Some good combination work between Bendtner and Eduardo on 78 minutes deserved a better finish but the Brazilian-born striker mis-hit his shot wide of the left post.
Bendtner did eventually break the deadlock on 83 minutes when he rose unmarked to head home a left-sided cross from Traore.
Newcastle almost levelled the scores within seconds as Martins sprung the offside trap but Senderos slid in to clear the ball just before it crossed the line with Fabianski well beaten.
With two minutes of regular time left on the clock, the Gunners doubled their lead when Denilson let fly with a 20-yard shot that winged its way into the top right corner of the net with Given nowhere near.