Joe Willock scored twice in the first half to leave the 13-time winners in control at the interval, and Alex Iwobi added a third with eight minutes remaining as the Gunners made it back-to-back wins for the first time in almost a month.
Blackpool acquitted themselves well against their more illustrious opponents and had the chances to threaten an upset, but they could ultimately have no complaints at the result as the gulf in class between the two sides told.
The chances flowed freely from the very start of the game, and most of them fell to Arsenal, who should have taken the lead after less than three minutes when Aaron Ramsey and Ainsley Maitland-Niles combined to set up Eddie Nketiah, who could only pick out the side-netting with just the keeper to beat.
Arsenal had been forced into a late change in defence after Laurent Koscielny picked up a back injury during the warm-up, being replaced by Carl Jenkinson, and that defence looked shaky throughout the first half as the goal-shy League One hosts posed regular problems.
The first of those arrived inside five minutes when Stephan Lichtsteiner - drafted into the middle following Koscielny's injury - backed off Armand Gnanduillet into the box, eventually leaving the striker with only the keeper to beat as Petr Cech made an important early save.
Arsenal were instantly back on the front foot in an open start to the game, and Nketiah squandered another golden chance to break the deadlock after seven minutes when he again fired wide after being teed up by Maitland-Niles.
The fast start to the match made an early goal seem inevitable, and sure enough it arrived after only 11 minutes when Willock reacted well to send a stooping header into an empty net after Ramsey's deflected free kick had bounced back off the inside of the post.
Unai Emery's side were slicing through almost at will at in the opening exchanges and could have had a second moments later when Jenkinson tried to nod Iwobi's cross back into the middle rather than going for goal himself.
Blackpool did eventually stem the tide of chances, though, and began to ask more questions of the Arsenal defence themselves as the first half wore on, with Chris Taylor drawing one save from Cech with a deflected shot on the turn.
Arsenal were limited to just long-range shots during that time and both Mohamed Elneny and Iwobi missed the target, but Blackpool's improvement was stopped in its tracks by a second goal for Arsenal with eight minutes remaining in the first half.
Again it was a poacher's finish from Willock, who this time tucked home at the back post after Nketiah had attempted to flick Jenkinson's low cross into the box towards goal.
Nketiah himself could have had a hat-trick in the first half, but he squandered his third big chance just before the interval when Mark Howard made a smart save to deny him from inside the area.
Blackpool had shown enough going forward to give them some encouragement despite their two-goal deficit at half time, and had they shown more composure in the final third they might have threatened a comeback in the second half, with Michael Nottingham failing to hit the target with two decent sights of goal before the hour mark.
The home side's belief began to sap away with each passing minute, though, and it was Arsenal that consistently looked more likely to add to the scoring in the final half-hour, with Elneny and Sead Kolasinac both missing the target with efforts from outside the area.
Willock had the ball in the back of the net 10 minutes from time, only to be correctly disallowed a hat-trick goal by the offside flag, although the assistant should have raised it again when Arsenal did score their third just two minutes later.
Ramsey should have scored himself with a toe-poke after being played through by Alexandre Lacazette, but he was denied by substitute Blackpool keeper Christopher Mafoumbi and the ball dropped to an offside Iwobi, who was left with a simple finish.
It could have got even worse for the Tangerines in the closing stages too, but Mafoumbi made two more good saves to deny Iwobi and Ramsey and keep the score down for the League One outfit.
There were no chances for consolation at the other end, though, as Arsenal eased to the victory and began their bid for a fourth FA Cup in six years in comfortable fashion.
BLACKPOOL (4-3-3): Howard (Mafoumbi 69'); Nottingham, Daniels, O'Connor, Bola; Taylor, Spearing, Guy; Delfouneso, Gnanduillet (Davies 83'), Feeney
ARSENAL (4-2-3-1): Cech; Jenkinson, Lichtsteiner, Sokratis, Kolasinac (Medley 83'); Elneny, Ramsey; Maitland-Niles, Willock, Iwobi (Saka 86'); Nketiah (Lacazette 64')