Unai Emery's side saw their 11-match winning run come to an end at Selhurst Park on Sunday, but it avoided falling short for a second game in a row, even if the performance left a lot to be desired.
An otherwise unremarkable first half was punctuated by Stephan Lichtsteiner's first goal for the club and 18-year-old Emile Smith Rowe seemingly wrapped things up in the 50th minute.
But Matteo Guendouzi's red card just before the hour for two cheap bookings boosted the visitors and they pulled one back through Paudie O'Connor soon afterwards.
It could not force the equaliser and their goalscorer was dismissed late on.
Arsenal eventually got a first shot on target in the 33rd minute and it provided them with the opening goal, as Lichtsteiner managed to nudge the ball into the bottom-left corner when stretching to reach Guendouzi's lofted pass.
Arsenal got itself another early in the second half – Smith Rowe finding the net from close range after Mark Howard parried Carl Jenkinson's miscued cross to the midfielder.
Blackpool was offered encouragement soon after when Petr Cech knocked a corner delivery against his own crossbar.
Guendouzi was then shown a second yellow for a needless tug on Jordan Thompson and Blackpool capitalised 10 minutes later, O'Connor heading home from Thompson's corner.
Cech attempted to dribble his way out of danger 21 minutes from time and was tackled by Jay Spearing, but Nathan Delfouneso's goal was disallowed for offside.
Blackpool's hopes of getting a second ended with O'Connor being shown a straight red six minutes from the end for a cynical tackle on Pierre-Emerick Aubameyang.