The man, who is in his 70s, shot the two suspected burglars Wednesday afternoon in a quiet subdivision of the Houston suburb of Pasadena. He confronted the men as they were leaving through a gate leading to the front yard of his neighbor's home.
No identities have been released.
Police say that just before the shootings, the man called 911 to say he heard glass breaking and saw two men entering the home through a window.
911: "Pasadena 911. What is your emergency?"
Caller: "Burglars breaking into a house next door."
A police spokesman says the man told the dispatcher that he was going to get his gun and stop the break-in.
Caller: "I've got a shotgun, do you want me to stop them?"
911: "Nope, don't do that. Ain't no property worth shooting somebody over, OK?"
The dispatcher repeatedly urged the man to stay calm and stay in his own home, reports CBS News correspondent Hari Sreenivasan.
911: "I've got officers coming out there. I don't want you to go outside that house."
Caller: "I understand that, but I have a right to protect myself too, sir, and you understand that. And the laws have been changed in this country since September the first, and you know it and I know it. I have a right to protect myself."
A Texas law strengthening a citizen's right to self-defense, the so-called "castle doctrine," went into effect on Sept. 1. It gives Texans a stronger legal right to use deadly force in their homes, cars and workplaces.
The telephone line then went dead, but the man called police again and told a dispatcher what he was doing.
Caller: "Boom. You're dead." (Sounds of gunshots) "Get the law over here quick. I've managed to get one of them, he's in the front yard over there. He's down, the other one is running down the street. I had no choice. They came in the front yard with me, man. I had no choice.
He shot one suspect in the chest and the other in the side.
Wednesday's shooting "clearly is going to stretch the limits of the self-defense law," said a legal expert.
If the absent homeowner tells police that he asked his neighbor to watch over his property, that could play in the shooter's favor, defense attorney Tommy LaFon, who is also a former Harris County prosecutor, told the Houston Chronicle. "That could put him (the gunman) in an ownership role."
The legislator who authored the "castle doctrine" bill says it was never intended to apply to a neighbor's property.
It "is not designed to have kind of a 'Law West of the Pecos' mentality or action," Republican Sen. Jeff Wentworth told the newspaper. "You're supposed to be able to defend your own home, your own family, in your house, your place of business or your motor vehicle."