With 54 league places separating the two clubs, an upset was unlikely and late goals from substitutes Olivier Giroud — his 13th of the season — and Santi Cazorla confirmed Arsenal’s superiority.
“In the first half we did the job and took the game to them in a serious way and played the way we know we can,” Gunners manager Arsene Wenger said.
Asked about a potential move for Schalke midfielder Julian Draxler, Wenger added: “Honestly no. That’s an illusion. We’ve no need to take players on the flank.”
Wenger had spoken of his determination to add to his haul of four FA Cup successes in the build-up to the game.
Arsenal’s last triumph in the competition came in 2005 when they beat Manchester United in the final, the last time the north London club won silverware of note.
And Wenger’s intention to avoid any risk of a shock was reflected in his team selection with Germany’s Mesut Ozil, the club’s record signing, included in a strong starting line-up.
It soon became clear the Premier League leaders would prove too hot to handle for their third tier opponents.
While the Gunners have spent much of the campaign fending off challengers at the head of the top flight, Coventry started the season with a 10-point penalty after falling into administration and forced to play their home games at Northampton Town, 31 miles away.
The way they have overcome the odds to climb to within 10 points off the League One play-offs has drawn praise for the players and manager Steven Pressley.
But while this meeting provided the 1987 FA Cup winners with a taste of what life used to be like before the club’s decline, it was never going to deliver a place in the next round.
Arsenal dominated from the opening moments, moving the ball around freely and giving a clear signal this would be a long evening for the visitors.
Jack Wilshere had already fired wide and Podolski missed a glaring opportunity by firing over from six yards before the German found the target to give Arsenal a 13th minute lead.
This time the forward showed much more composure, collecting a pass from Ozil and rounding Coventry goalkeeper Joe Murphy before slotting home left-footed.
The visitors’ response was impressive with skipper Carl Baker drawing a fine save from Lukas Fabianski with a long range effort four minutes later.
But it was largely one-way traffic and there was little surprise when the Gunners doubled their lead in the 28th minute.
Serge Gnabry whipped in a corner from the left towards Nicklas Bendtner, who was allowed to flick on towards the unmarked Podolski who headed home from close range.
The concern for Coventry was that they would find themselves on the end of a rout, but Pressley’s side managed to see out the remainder of the half without conceding again.
Coventry returned for the second half showing much more purpose and twice threatened to force their way back into the game early in the second half through Leon Clarke.
The striker initially found his way behind the Arsenal defence but his angled shot was denied by Fabianski then minutes later, Clarke saw a right foot effort bounce to safety off the post with the keeper beaten.
That was enough to remind Arsenal there was still work to be done and while Wenger’s side soon regained control of the game.
That allowed Wenger the opportunity to hand a debut to highly rated midfielder Gedion Zelalem, the 16-year-old Germany Under-17 international, midway through the second half.
Giroud then added a third goal after appearing as a late replacement for Podolski, sweeping home in the 85th minute from Kieran Gibbs’ low cross.
And Cazorla followed up a Murphy save to make it four in the final minute of normal time.