Hirtz's previous stint as a council member was also a factor in the decision, as Councilman Shawn O'Connell said he desired that "the next person be experienced."
Hirtz last served on the council in the mid-1990s.
Reached by phone after the meeting, Hirtz, 64, said she was prompted to seek office at the urging of close friends.
"Honestly, it came from a group of people who had an organized plan to talk me into submitting a letter of interest," she said.
Hirtz owns an outdoor lawn equipment store and said her experience as a business owner through various economic cycles will help her make decisions for a city that is mired in deficit spending and other financial woes.
"I'll bring those skills to deal with the problems in the best way possible," Hirtz said.
The council could have chosen to hold a special election, but that would have cost the city up to $285,000.
The council on Jan. 22 was deadlocked on who to appoint.
O'Connell and Councilman Ed Palmer supported Hirtz. Mayor Deborah Robertson and Councilman Joe Baca Jr. threw their support behind Rafael Trujillo, who is on the Recreation and Parks Commission and was third behind Palmer and O'Connell in the November council election.
Robertson said at Monday's meeting that her support for Trujillo was no knock on Hirtz.
She said her decision Monday to vote for Hirtz was to send a message "that we are unanimous."
The council has shuffled seats in recent months, after Robertson, a former council member, defeated former Councilman Ed Scott for the mayor's seat, following then-Mayor Grace Vargas' decision to not run again.