The clash between the FA Cup winners and the Premier League holders was comfortably won by the former, who added another piece of silverware to their trophy cabinet after ending their nine-year drought with success against Hull City last May.
Arsenal took the lead in the 21st minute when the ball broke to Santi Cazorla on the edge of the box and he created a yard of space with a fine feint away from Gael Clichy before driving a low shot across Willy Caballero and into the bottom corner.
Arsene Wenger’s men doubled their advantage shortly before the interval courtesy of a classy goal from FA Cup final hero Aaron Ramsey, with the Wales international receiving the ball from Yaya Sanogo, fooling Matija Nastasic with a neat dink and then drilling beyond Caballero.
Giroud stepped off the bench at the interval and netted an outstanding third on the hour mark, sending a dipping effort from long range over Caballero after holding off Bruno Zuculini some 25 yards out, with the City man having only joined the fray seconds earlier.
Regardless out of the outcome, rival managers Manuel Pellegrini and Wenger will know much sterner tests lie ahead before they hand out the major honours again in nine months' time.
Arsenal made most of the early running, as Alexis Sanchez combined well with Jack Wilshere.
When City did get a corner, former Gunner Samir Nasri was loudly jeered by the Arsenal fans behind the goal - the French midfielder having labelled supporters of his old club "stupid" for their continued jibes since his big-money move three seasons ago.
Arsenal maintained pressure down the right, from where Debuchy - signed from Newcastle to replace Bacary Sagna - delivered a couple of decent crosses which were just too high for Yaya Sanogo, deployed as a central striker.
City’s first chance came on 14 minutes when Nasri crashed a shot at Debuchy, which the defender blocked with his chest at point-blank range.
The FA Cup winners were soon on the offensive again, this time left-back Kieran Gibbs marauding into the penalty area before his shot was blocked by Gael Clichy, another former Gunner.
Arsenal went ahead after 21 minutes as Sanogo and Wilshere worked some space at the edge of the City penalty area, before the ball broke left to Cazorla, who sidestepped Clichy before sliding a low shot back across Caballero.
Sanogo then dragged a shot wide from the edge of the City penalty area as the Premier League champions were opened up again.
City showed a bit more invention as the first half drew towards a close, but lacked any real penetration in final third.
Edin Dzeko powered his way into the left side of the Arsenal penalty area, but his cutback towards Stevan Jovetic was blocked.
Arsenal doubled their lead after 42 minutes with a simple goal, yet one of the highest quality.
Sanchez's ball from the right was held up at the edge of the City box by Sanogo. The France forward showed great strength to lay a pass back to Ramsey, who stepped past his marker before clipping the ball into the net and wheeling away in celebration - just as he had done at the other end in the FA Cup final here some 12 weeks ago.
The second half saw the expected substitutions by both teams.
Arsenal replaced Sanchez with Alex Oxlade-Chamberlain, Sanogo with Giroud and Laurent Koscielny with Nacho Monreal. For City, David Silva replaced Nasri.
The Premier League champions looked more lively following Silva's introduction and Jovetic saw his header strike the post following a deep right-wing cross by Jesus Navas.
Arsenal goalkeeper Wojciech Szczesny then produced a good save as he stopped a low effort from the Montenegro forward, but, on the hour, Giroud cracked in a sublime third.
There seemed little on for the France forward when he picked the ball up some 25 yards from goal, surrounded by three defenders. But that did not matter as Giroud promptly fired in a rising effort which nicked off Matija Nastasic and into the roof of the net.
The closing stages were low key, but the end result will nevertheless give Arsenal fans hope they may just be able to last the distance with City when the action gets under way for real next weekend.