The night's two other ties between West Ham United and Stoke City and Aston Villa and Burnley went in extra-time, with both West Ham and Villa progressing without the need for penalties.
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Despite the lure of a Europa League place for the winners of England's "third trophy", most clubs continue to treat it as a chance to try out young players and give run-outs to squad members - as well as those on the comeback trail from injury.
That certainly worked out well for Arsene Wenger.
This season the Arsenal manager has actually fielded stronger teams than in recent years but his line-up at St James' Park still showed nine changes from their weekend Premier victory over Manchester City.
Newcastle, whose virtual reserve team knocked out a second-string Chelsea in the last round, also made nine changes from their weekend win at West Ham United.
Both sides had good chances in an open first half, with Alan Smith hitting the bar for Newcastle, before Arsenal grabbed the lead just ahead of the interval with a somewhat bizarre goal.
Bendtner, making his first start of the season after recovering from a groin problem, thumped a header goalwards and Ryan Taylor's attempt to clear it ended with the ball rebounding off his goalkeeper Tim Krul and over the line.
Walcott, in his first start since injuring his ankle playing for England in early September, broke clear to put Arsenal two up eight minutes into the second half but Newcastle were furious that Bendtner, who was returning from an offside position, collided with home defender Mike Williamson, taking him out of the action.
Bendtner completed his busy night when he collected a pass from substitute Cesc Fabregas to cut in and curl home an excellent third goal four minutes from time with Walcott adding a breakaway fourth in stoppage-time.
West Ham briefly lifted some of the gloom surrounding the Premier League's bottom club with their win.
Kenwyne Jones headed Stoke into an early lead, Scott Parker equalised six minutes from time and Mark Noble proved the key man in extra-time as he set up goals for Manuel da Costa and Victor Obinna.
Emile Heskey came off the bench to fire Villa ahead in the 86th minute of their game against Burnley but Clark Carlisle equalised in the last minute.
Winger Stewart Downing blasted Villa back into the lead after six minutes of extra-time but they had to hang on for the last 20 after Marc Albrighton was sent off.
Birmingham City, Wigan Athletic, West Bromwich Albion, Manchester United and Championship Ipswich Town were already through to the last eight and the draw for the quarter-finals will be made on Saturday.
