Smith said the suspect had suffered a gunshot wound through his hand, though it's unclear when he was shot.
"He starts coming toward the front door, then he turns around and lunges at the pastor and was able to disarm the pastor, it appears at this time", Smith said.
Gov. Greg Abbott (R) released a statement regarding the innocent saying, "Our hearts are with the victims and the families of those killed or injured in this bad tragedy".
He then stole the pastor's vehicle and headed onto the Interstate where he drove at speeds of up to 120mph before being caught in Harrison County with a gunshot wound to his hand. He then fled into the nearby woods on foot, evading law enforcement before allegedly breaking into the Starrville Methodist Church and hiding overnight.
Sgt. Larry Christian, who is the Smith County Sheriff's Office spokesman, stated that the shooter has been caught and is in custody.
Smith said police were initially pursuing the man because he was suspected of brandishing a shotgun through the sunroof of a Volkswagen Jetta he was driving Saturday.
He said that no services were going on in the church when the 21-year-old old suspect opened fire.
There were two other individuals inside the church during the incident.
More quakes hit Croatia over the night and Thurs morning
It was felt as far away as Graz in southern Austria, the Austria Press Agency reported. The BBC reported a 12-year-old girl as the lone fatality so far from Tuesday's quake .
Smith declined to identify the pastor, the other people injured or the suspect.
It was cold, and the church was likely convenient shelter, Smith said.
The victim, Pastor Mark McWilliams was found dead at the Starrville Methodist Church near Winona.
The shooting, at Starrville Methodist Church in Starrville, about 100 miles east of Dallas, occurred just after 9 a.m. when only about four people were in the church, authorities said.
A tweet from the scene showed the police response at the church.
Texas has seen other church shootings in the past.