France striker Giroud had not scored in his 11 previous games but made the most of a terrible back pass after 40 minutes and then doubled the lead with 20 minutes remaining following a sharp volley from close range.
Walcott sidefooted the ball home to make it 3-0 before his low drive capped Arsenal's first win in six games.
Victory though came at a cost for Arsenal, who face Watford in the last eight, as defenders Per Mertesacker and Gabriel and midfielder Aaron Ramsey were forced off through injury.
"I'm a bit shocked, we lost our two centre backs in the game and we lost Aaron Ramsey," manager Arsene Wenger told BT Sport following his team's sixth match in a hectic 18-day spell.
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"Mertesacker has a cut on his eye and a bit of concussion but he should be fine and Gabriel looks alright. Ramsey, I'm a bit more concerned about because it's a muscular thigh injury."
EXTRA IMPORTANCE
The competition has taken on extra importance for Arsenal with their Premier League title challenge faltering in recent weeks and their Champions League hopes in tatters after Barcelona left the Emirates Stadium with a 2-0 win two weeks ago.
The pressure has mounted on Wenger with the FA Cup now seemingly the club's best hope of silverware.
Wenger changed six players following their 2-2 draw at Tottenham Hotspur in the north London derby on Saturday and his side dominated possession in the first half.
They took the lead when Hull's David Meyler failed to look up before playing a blind back pass across his own goal, Giroud intercepting and finishing calmly beneath keeper Eldin Jakupovic.
It was almost 2-0 moments later when Kieran Gibbs rattled the bar from distance while Mohamed Elneny forced a superb save from Jakupovic at the start of the second half with the keeper athletically tipping the ball over the bar.
Giroud then expertly volleyed home a cross from Walcott before the latter opened his account when he found the far corner following a brilliant pass by Joel Campbell.
Walcott, who was captain for the night, made it 4-0 when his effort was deflected into the net off Hull defender Alex Bruce.
(Reporting by Toby Davis; Editing by Tony Jimenez)
