The pair were parked nearby when a radio call came in for officers to respond to a shop robbery.
But a review of their in-car camera footage showed they had been playing Pokémon Go and chose to pursue a nearby Snorlax - a relatively rare catch - instead of providing back-up.
The pair denied playing the game but were sacked after an investigation.
Details of the case emerged when the most recent documents about their appeal - which was dismissed - were spotted by Axios.
After ignoring a radio call for back-up, "for approximately the next 20 minutes, [video] captured [the] petitioners discussing Pokémon as they drove to different locations where the virtual creatures apparently appeared on their mobile phones", the documents say.
Louis Lozano and Eric Mitchell had been on patrol when Macy's department store was robbed, on 15 April 2017.
Another officer, Capt Davenport, who also heard the call, could see the shop - and another police car parked in a nearby alley, the court documents show.
Those nearby officers did not respond to the call, so Capt Davenport did so himself - and saw the other police car reverse down the alley and leave the area.
The two officers later told a sergeant who had been trying to contact them to provide back-up they had not heard the radio.
But the in-car camera footage revealed they had discussed the call and decided not to respond.
Instead, five minutes later, they could be heard talking about catching Pokémon.
"Officer Mitchell alerted Lozano that 'Snorlax... just popped up [at] 46th and Leimert'", the documents say.
The pair then left in that direction to embark on a 20-minute gaming session and discussion.
They could be heard talking about the successful capture of Snorlax and how difficult the battle with Togetic - another Pokémon - was.
"The guys are going to be so jealous," Officer Mitchell said.
Both officers denied gaming on duty, telling the investigating detective Officer Mitchell had been reading aloud from a text group of other players "bragging about their scores".
"Det McClanahan determined [the] petitioners were not being truthful," the court documents say.
A subsequent board hearing into misconduct found the pair guilty of:
* failing to respond to a robbery call
* making misleading statements
* failing to respond to the radio when contacted
* playing Pokémon Go on duty
* making false statements under investigation
The "petitioners admitted leaving their foot-beat area in search of Snorlax but they insisted they did so 'both' as part of an 'extra patrol' and to 'chase this mythical creature'," according to the court.
Their representatives had argued in-car recordings were not supposed to be used to record private conversations and should not have been used as evidence - but that was denied.
The pair then went to court, where their case was rejected.
The appeal court also rejected the case, saying the two former officers' rights had not been violated.