Trevon Kyron Thomas, 24, from Melford Road, Bilborough, fired three shots at Pc Rachael Bown when she was called to a burglary in Nottingham.
During the trial, Thomas said he had fired the gun accidentally as he was overcome by CS gas sprayed at him by Pc Bown's colleague.
He was also found guilty at Nottingham Crown Court of possessing a firearm.
During the trial Thomas, who is originally from Trinidad and entered the UK in February 2000 on a six-month visitor's visa, told the jury he was carrying the Browning 9mm pistol, loaded with 13 rounds of ammunition, for "protection".
He said he had previously witnessed a friend shot dead in the city and had been injured by a firearm himself a few years previously.
But the jury, who were not told about Thomas' immigration status, returned a unanimous guilty verdict on Tuesday.
|| Trevon Thomas is a dangerous
man...he showed contempt for human life
Det Ch Insp Dave Giles
The jury did not return a verdict on a third charge of possession of a firearm with intent to resist arrest.
Ms Bown, 24, was shot in the stomach while on patrol in the Lenton area of Nottingham on 14 February 2006.
She suffered life-threatening injuries when she was shot below her body armour, while investigating reports of a burglary, and has still not returned to work.
Speaking after the trial, Pc Bown's father, Martin Bown, spoke about the night his daughter was shot.
"On that dreaded night we opened the door to be told of every parent's worst nightmare.
"No-one knows the horror, shock and worry that my wife and our two other daughters suddenly found ourselves in.
"Fortunately we were very lucky," he said.
In court, Thomas said he had fled the scene of the shooting on 14 February as police started to question him, because he was scared he would be caught with a firearm.
Det Ch Insp Dave Giles from Nottinghamshire Police said: "Trevon Thomas is a dangerous man. He went out that night with a firearm.
"When compromised by uniformed officers, he did not hesitate to use it. He showed contempt for human life," he said.
Det Ch Insp Giles added he hoped the guilty verdict would act as a deterrent to others carrying guns.
Police caught up with Thomas as he sat on a plane for Trinidad at London's Heathrow Airport on 17 February.
Thomas will be sentenced at a later date.
Pc Beshenivsky, 38, was shot dead after a bungled robbery in November, 2005.
Yusuf Abdillh Jamma, 20, of Whitmore Road, Small Heath, Birmingham, had admitted robbery and two firearms offences but had denied murder.
Brothers Faisal and Hassan Razzaq were cleared of murder but convicted of manslaughter and Raza Ul-Haq Aslam, 25, was cleared of manslaughter and murder.
A fifth man has already pleaded guilty to murder.
Jamma was convicted following an 11-week trial at Newcastle Crown Court.
He was found guilty of possessing a MAC-10 machine gun and a 9mm pistol with intent to endanger life, and two counts of possessing the firearms. He admitted robbery part-way through the trial.
Aslam, of St Pancras Way, Kentish Town, north London, was cleared of all charges except for robbery, and the jury will be continuing its deliberations on that charge on Tuesday.
Brothers Faisal Razzaq, 25, and Hassan Razzaq, 26, from Sebert Road, Forest Gate, east London, were found guilty of robbery but cleared of possessing firearms with intent to endanger life.
Muzzaker Imtiaz Shah, of no fixed address, previously admitted murdering Pc Beshenivsky.
Shah also admitted robbery and firearms offences.
He was cleared of the attempted murder of Pc Beshenivsky's colleague Pc Teresa Milburn earlier in the trial.
Pc Beshenivsky was shot and killed as she arrived at the Universal Express travel agents in Bradford city centre on 18 November 2005, the day of her youngest daughter's fourth birthday.
Pc Milburn was seriously injured when she was gunned down in the street as the robbers escaped with little more than £5,000.
Jamma told the jury he fired the fatal shot from the 9mm pistol, but did not intend to kill Pc Beshenivsky.
He repeatedly denied the prosecution's suggestions that his version of events was a lie to help Muzzaker Shah get off the attempted murder of Pc Milburn.
Aslam told the court he had no part in the robbery or murder and was simply "in the wrong place at the wrong time."
He said he believed he was entitled to a £100,000 reward for helping police catch Pc Beshenivsky's killers because he rang Crimestoppers and passed on information.
Faisal Razzaq admitted he was round the corner from the travel agents when the shootings took place but said he was at a takeaway and denied acting as a look-out.
Hassan Razzaq was the only defendant who chose not to give evidence at the trial.
Two other suspects, Jamma's brother Mustaf and a man called Piran Ditta Khan, remain on the run from police.