Rogers, who was identified by her mother, killed the children before stuffing them inside a closet and a suitcase, Phoenix Police Sergeant Trent Crump said.
Police say the 29-year-old mother to the three boys stabbed herself in the neck and abdomen, claiming she was pregnant.
She is in a critical condition in hospital but is expected to survive.
The children's grandmother, Tanella McCoy, said Rogers was a 'good mother' and did not appear to be having any problems with her children.
'I don’t know what to feel right now. I don’t know where to go, I don’t know where to turn,' Ms McCoy told The Arizona Republic.
'My daughter knew beyond a shadow of a doubt that I would take her kids ... because there were times she would talk to me about leaving for the summer.'
McCoy said Avery was a 'very good baby', adding that Jeremiah was her 'muscleman' and Jaikare was a 'book scholar' with a bright future.
Sgt Crump said Rogers' brother got off from work and returned to the house - which is owned by the children's grandmother - at around 2am on Thursday.
He immediately called 911 and went to get towels to help her wounds, but then she attempted to drown herself in the bathtub, he said.
Rogers reportedly told her brother that she was pregnant while stabbing herself in the abdomen. Officials are still trying to determine if that was true or not.
When the woman was being treated by emergency crews, she told them that her children were with someone else, Sgt Crump stated.
However, when authorities entered the home, they made the grim discovery of finding the two children stabbed to death inside of a closet.
Upon a second search and after speaking with family members, they went back inside the home and found the infant inside of a suitcase within the closet.
It was an 'absolutely horrific scene for the officers and the brother,' Crump said.
Rogers is currently hospitalized in critical condition, but is expected to survive, Crump said.
'She will be in the hospital for some time with some very serious self-inflicted injuries,' Crump said. 'It's a murder investigation at this point.'