The jury heard how an ambulance was called to the property at about 5.30pm on Wednesday, April 13, when Eli stopped breathing.
He was taken to Medway Maritime Hospital where a paediatrician noticed a number of bruises that were not believed to have been accidental.
It was reported to Kent Police, with detectives from the serious crime directorate launching an investigation.
Medical experts found Eli's brain injury would have occurred almost immediately before he collapsed, while they said the bone fractures would have been inflicted in at least five separate incidents since February 2016.
Both Cox and Shepherd - who calls himself "Pickle" - denied being users of cocaine and amphetamine, despite five wraps of the latter substance being found by police in a garden shed at their home.
They moved in together in November 2015 after they started dating that summer.
The pair are due to be sentenced at the same court at a later date once psychiatric reports are prepared.
Post-mortem examinations showed Eli had oxygen deprivation to his brain, suggesting he had suffered a trauma, bleeding around his optic nerves and a brain injury.
As previously reported, Cox told police she called an ambulance after seeing Eli lifeless on the bed with "ooze coming out of his nose".
She also told officers that Shepherd - who called himself "Pickle" - was performing adult CPR on him.
Cox's friend and neighbour Bonnie Bolton is trained in first aid and rushed into the home in an effort to save the baby.
She told Shepherd to stop the CPR, pushed him aside and put a finger into Eli's mouth to check if his airway was clear, but found no obstruction.
The 999 operator gave her instructions to perform CPR, which she did until the ambulance crew arrived.
Miss Bolton remembered Cox repeatedly saying that she thought Eli was dead.
She also said: "Pickle, what have you done?"
Miss Bolton claimed that more than once Shepherd said: "I will get the blame for this. They will blame me."
The jury was also told Shepherd explained to paramedics that Eli had been unwell for a number of days and had vomited.
He also claimed that the baby's lips had turned blue after he had stopped breathing.
However, the two paramedics in the ambulance could not remember the smell of vomit or any signs of it on Eli, the court heard.
The oldest of his fractures was possibly from between seven to nine weeks before his death. A hair sample showed he had been "regularly exposed to amphetamine and occasionally exposed to cocaine", Ms Knight added.
Shepherd told police that neither he nor Cox had deliberately or accidentally injured Eli or lost their temper with him.
The court heard there was a long, thin wooden stick, which was dubbed "Pickle's beating stick".
But the couple said it was banged to get the dogs into the garden and was not used as a weapon.
Libby Clark, from the Crown Prosecution Service (CPS), said afterwards: "This has been a difficult case to prosecute due to the complex medical evidence and challenges in establishing the involvement of either or both of the defendants in relation to the fatal injury caused to Eli.
"When the trial started, our case was that either Danny Shepherd or Katherine Cox had caused Eli's injuries and the death, or were aware that there was a significant risk of serious physical harm being caused to him, and failed to take reasonable steps to prevent this.
"During the course of the trial and in light of the evidence given, it became possible to say that Danny Shepherd was the perpetrator of the injuries to Eli, including the assault which led to his death.
"The fatal injury and older fractures identified by one of the medical experts showed very significant similarities.
"This considerably undermined the defence case that they were caused by another person."
Senior investigating officer Detective Inspector Ivan Beasley added: "The death of a child is never anything less than tragic but the circumstances behind Eli Cox's passing are especially upsetting for those of us who share a compassion for others.
"None of us will ever understand what compels people to cause harm to children, and it is unfortunately true to say that Eli suffered more than most and was robbed of his life before it had barely begun.
"Katherine Cox and Danny Shepherd maintained their innocence throughout but the jury saw through their lies.
"Only they know the true extent of the abuse Eli was put through, which is simply unthinkable to most members of society including parents who would do anything to protect their children from harm. "
