Walcott's brace, an own goal from Newcastle reserve keeper Tim Krul and a Nicklas Bendtner strike settled the tie for Arsene Wenger's men, riding high after last weekend's victory over Manchester City. Wenger was left purring over the contribution of Walcott, scoring his first goals since returning from injury sustained on England duty last month.
"Walcott is more composed in front of goal this season. His first touch is better. He is an intelligent boy and because of that he will always improve," Wenger told Sky Sports 2. "He was flying at the start of the season and now he is just coming back from injury. You can see today that he is ready to go to another level."
Both Arsenal and Newcastle made nine changes from the teams which scored impressive away victories in the Premier League last weekend. Yet Wenger was still able to field a starting XI featuring no fewer than seven internationals - reflecting the Arsenal manager's stated determination to end the Gunners' five-year trophy drought this year.
Arsenal's hunger was apparent from the outset, the visitors sweeping forward relentlessly in search of an early goal in the opening 10 minutes, with Walcott, Bendtner and Carlos Vela all threatening. But Newcastle also could have taken the lead in the opening period, Nile Ranger missing a gilt-edged chance before Alan Smith saw a shot tipped onto the bar by Arsenal's understudy keeper Wojciech Szczesny.
Arsenal went 1-0 up with a farcical own goal on the stroke of half-time, Krul inadvertently heading a clearance from Ryan Taylor into his own net. Walcott made the game safe eight minutes into the second half, bursting clear to double Arsenal's lead with a goal that drew protests from Newcastle, who complained that defender Mike Williamson had been fouled by Bendtner.
The goal knocked the stuffing out of Newcastle and Arsenal gradually took control of the second half, Walcott and Bendtner scoring in the final ten minutes to give the scoreline a lop-sided look.
Extra-time saves Hammers and Villains
At Upton Park, West Ham United came from behind to defeat Stoke City 3-1 in extra time after trailing for most of the match. Trinidad and Tobago international Kenwyne Jones looked to have headed Stoke into the last eight after only six minutes, giving his team a 1-0 lead.
But Hammers skipper Scott Parker forced extra-time with an 84th-minute equaliser before Manuel da Costa put the home side ahead on 96 minutes. Substitute Victor Obinna completed the scoring two minutes from time.
There was more extra-time drama at Villa Park, where Aston Villa overcame spirited resistance from Championship side Burnley to win 2-1. Emile Heskey looked to have settled the contest when he put Villa 1-0 up in the 86th minute only for Clarke Carlisle to level three minutes later.
Yet winger Stewart Downing rifled in a 20-yard effort to restore Villa's lead on 96 minutes to break the deadlock. Villa were forced to endure a nervous finale after Marc Albrighton was sent off for a professional foul but Gerard Houllier's men hung on for victory.
The quarter-final draw takes place on Saturday.