Goals from the Frenchman, Alex Oxlade-Chamberlain, Andrey Arshavin, Ignasi Miquel and a Theo Walcott double saw the hosts through, with Callum Bell grabbing a consolation strike
The Frenchman gave the hosts the lead five minutes before half-time with a chip over the goalkeeper and other strikes from Alex Oxlade-Chamberlain, Andrey Arshavin, a double from Theo Walcott and one for Ignasi Miquel settled the game, with substitute Callum Bell notching a consolation strike for the visitors.
Arsene Wenger, as expected in the League Cup, named a young line-up though some bigger names, including Giroud, Walcott and Arshavin, also started, while Oxlade-Chamberlain was in midfield with Nico Yennaris and Francis Coquelin.
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The first chance of the game fell to the visitors, after Frank Moussa got down the line before clipping a cross into the box. Stephen Elliot headed wide, with team-mate Gary McSheffrey appearing to get in his way.
But the hosts were not on the back foot for long and really should have been ahead through contract rebel Walcott. The ball fell kindly for the winger inside the area but he totally missed the ball after a wild kick at it.
Arsenal, and Arshavin in particular, began to step it up a gear, though the final ball was still lacking. Shots from the edge of the box were blocked or crosses were overhit, while Coventry were forcing Martinez into some work, though most of it was fairly routine stuff for the Gunners keeper.
But in the 39th minute, Arsenal did take the lead, with Giroud scoring his first for the club. The French striker was played in with a great ball from Coquelin and, after taking a touch, he elegantly chipped the ball over the onrushing Joe Murphy.
The Gunners almost had an acrobatic second minutes later when Giroud flicked on Walcott's cross for Miquel to send an overhead kick just wide of Murphy's goal but they had to be content with a one-goal lead at half-time.
Five minutes into the second period, the hosts had a great chance to extend their advantage from the penalty spot after Arshavin was bundled over by Jordan Clarke after the defender misplaced a header back to Murphy.
After a momentary pause to remove two pitch invaders, Giroud stepped up for the spot kick but his effort was well saved by Murphy, low to his right-hand side.
From the resulting corner, Miquel again came close, hitting the top of the bar with his header from Walcott's cross. But again, the Gunners were not to be denied, as they extended their lead in the 57th minute.
Oxlade-Chamberlain cut in from the left before playing a nice one-two with Santos and hit a scorcher from 25 yards into the top corner past the helpless Murphy.
And the Gunners soon put the game beyond doubt, with Arshavin being played in by Giroud before hitting a low shot past Murphy to all but seal their progression into the next round with half-an-hour to play.
With a little over 15 minutes to go, Walcott also got on the scoresheet, cutting in from the right wing, driving at the defence before lashing a shot into the far corner.
But Coventry did get something for their travelling fans to cheer, sneaking a consolation as substitute Ball got in between Miquel and Djourou unnoticed to tap home from six yards.
The Gunners responded immediately, however, with Miquel making amends for his sloppy play at the back to nod home Arshavin's cross.
Walcott completed the rout in added time, this time cutting in from the left in a similar fashion to his first before curling a shot into the far corner to the delight of the home fans still in the ground.