An unfortunate Tim Krul own goal handed Arsenal a half-time lead and a controversial second from Walcott gave them some breathing space, but it was harsh on the Magpies.
However the two goals took the life out of Chris Hughton's side and there was nothing unfortunate or controversial about Bendtner's 83rd-minute strike or Walcott's cool finish two minutes from time.
If there was a touch of misfortune about the opening goal in first-half injury time - Ryan Taylor's defensive header hit the unwitting Krul and dropped into the net - there was more than a hint of injustice about the second when Nicklas Bendtner, who had run from an offside position, collided with Mike Williamson as he attempted to get to Walcott.
Alan Smith had earlier hit the bar as the home side recovered from a whirlwind start by the visitors, but the home fans among a crowd of 33,157 left hoping for a very different result on Sunday when Sunderland make the short trip to Tyneside in the Premier League.
Chris Hughton had made no secret of the fact that the Carling Cup was little more than a pleasant distraction during a season in which the only objective is top-flight survival.
In the circumstances it was little surprise that he rested nine of the men who fought out a 2-1 win at West Ham on Saturday evening with one eye on the weekend.
Arsene Wenger made the same number of changes, but the relative strengths of the respective squads was made abundantly clear when the Frenchman was still able to name the likes of Laurent Koscielny, Denilson, Walcott and Tomas Rosicky in his starting line-up.
Wenger has given the competition a higher priority this season and his side could have been all but in the last eight within five madcap minutes of a thrilling first-half.
Carlos Vela forced a save from Krul within 22 seconds of kick-off, and the Dutchman was in action again with five minutes gone to deny Bendtner, who had already seen Williamson block two efforts from the Dane.
In the meantime, Newcastle midfielder Haris Vuckic had shot into the side-netting, and as the half wore on, the Magpies started to come into the game.
Indeed, they could have taken the lead themselves with 14 minutes gone with the visitors' goal coming under intense pressure.
First Nile Ranger ran on to Danny Guthrie's ball over the top and rounded keeper Wojciech Szczesny, only for Koscielny to block his shot.
But Arsenal failed to clear their lines and when the ball fell to Smith 25 yards out, he unleashed a thunderbolt which looked destined for the back of the net - he is yet to score a competitive goal for the club - until Szczesny managed to tip it on to the bar.
As the game settled down, Newcastle were repeatedly at full stretch, but coping as they worked hard to close down space in midfield and plug the gaps at the back.
Bendtner twice shot straight at Krul and Emmanuel Eboue fired wastefully into the side-netting during the closing minutes of the half, and it looked like the sides would go in level at the break.
But with only seconds of added time remaining, the home side's luck deserted them.
They half-cleared Walcott's corner, but when Rosicky helped the ball back into the danger area, Bendtner headed towards goal, where Taylor's attempted clearance hit Krul and rebounded into the net.
Newcastle went close to an equaliser four minutes after the restart when Ranger's persistence forced Koscielny to concede a corner.
James Perch met Guthrie's set-piece with a firm header, but guided the ball just over.
But their hopes were dashed when the Gunners extended their lead in controversial fashion with 53 minutes gone.
Walcott ran on to John Djourou's defensive header from an on-side position, but Bendtner, who had been offside, appeared to block Williamson as he attempted to cover across.
However, referee Andre Marriner allowed play to continue and Walcott calmly chipped Krul to make it 2-0 with Newcastle protests counting for nothing.
Ryan Taylor might have pulled one back eight minutes of time, but was denied by Szczesny from point-blank range, but Bendtner made sure seconds later with a fine right-foot finish.
Szczesny clawed away Taylor's 86th-minute free-kick to deny Newcastle any reward for their efforts, and Walcott wrapped up the win with a pacy run and finish two minutes later.