Already on a warning, Leandro Trossard took a leaf out of the wrong Rice book and got himself sent off with a moment of utter madness, kicking the ball away having just given away a free kick for a nudge on Bernardo Silva.
On-field referee Michael Oliver had no choice but to dismiss the Belgian, whose dismissal was met by disbelief and a shaking head from Mikel Arteta, and an apparent ironic laugh from coach Carlos Cuesta.
A dumbfounded Trossard was welcomed off the pitch with open arms by Arteta, although the Spaniard may have been secretly seething at his attacker for his brainless decision, right at the end of an otherwise successful first half for Arsenal.
Gooners felt particularly aggrieved at Rice's red three weeks ago for the fact that Joao Pedro got away with kicking the ball away without a booking earlier in the game, and there was an argument that Jeremy Doku could have also earned a caution on Sunday for a similar offence.
However, Trossard could have no complaints about his punishment, and the Belgian will now serve a one-match suspension, as is the rule for red cards stemming from two bookable offences.
Trossard banned for Bolton Wanderers clash
Unlike yellow card suspensions, where a player picks up a ban for accumulating five, 10 or more bookings over the course of a certain number of games, red cards are not competition-specific.
As a result, the 29-year-old has now been ruled out of contention for Wednesday's EFL Cup third-round match against Bolton Wanderers, as suspensions from red cards count across all tournaments.
Trossard will therefore be back in the ranks for next weekend's Premier League clash with Leicester City, and it would not have been a surprise to see him omitted from the XI for the Bolton clash anyway, with Arteta likely to make several changes.
Trossard's dismissal rounded off a chaotic first half at the Etihad Stadium, where Erling Haaland's 100th goal for Man City deservedly put the Premier League champions ahead, but the hosts then lost midfield fulcrum Rodri to what looked like a severe knee injury.
Rodri's substitution breathed new life into Arsenal, who drew themselves level from a fabulous Riccardo Calafiori curler on his full Premier League debut, although City were incensed at Oliver for allowing the Gunners to take the free kick quickly.
The same combination that led to Arsenal's winner at Tottenham Hotspur - Bukayo Saka and Gabriel Magalhaes - then came good from another successful corner routine to put the visitors ahead, although the former was then sacrificed for Ben White at half time as Arteta reverted to an all-out defensive shape.