Police said Cox used his own gun, believed to be a 9 mm, to fire the shots at Fletcher.
Police were able to convince Cox to let two officers enter the home to rescue Fletcher. Sam Smith of the Charles Town Police Department and Ranson Police Chief Bill Roper went into the house, police said Tuesday.
Fletcher was pulled out of the house and two young children who were inside also were freed, police said.
Charles Town Police Chief Barry Subelsky said it was an extremely dangerous situation for Smith and Roper.
"He (Cox) could have just been luring them in," Subelsky said. "You went beyond duty when in the first few moments you decided not to let a man die in the dirt," Subelsky said.
Capt. Rob Blair of the West Virginia State Police said the actions of Sigulinsky, Smith and Roper probably saved Fletcher's life.
"Roper did an excellent job. He really put himself in harm's way," Blair said.
Roper declined to comment in detail about the incident, partly because of ongoing investigations.
"We just helped," Roper said.
Fletcher, a four-year veteran of the sheriff's department, was responding to the Orchard Hills home for a call about a man - who police identified as Cox - trying to break in through a back door using a shovel.
Police said Cox had been asked to leave the house behind Ranson Square off Mildred Street in Ranson by his girlfriend on Valentine's Day and he was despondent.
Police said that when they arrived Cox was carrying toolboxes from the house and Fletcher told Cox to put them down.
Fletcher followed the man into the house and the officer was shot in the left shoulder and left lung, Jefferson County Sheriff Everett "Ed" Boober said. Police initially believed Fletcher was shot three times but Boober said Tuesday it was only twice.
One shot was to the shoulder area and the other shot went through Fletcher, nicking his lung, Boober said.
Cox would not leave the house despite extensive negotiation efforts, and a six-hour standoff ended when police stormed the house after shooting tear gas canisters in the house.
Cox was found under a pile of clothes in a closet and fired once, police said. A special response team member returned fire but it was not clear whether the shot Cox fired or the shots fired from police killed him, police said.
Fletcher underwent surgery Tuesday at Washington (D.C.) Hospital Center to repair damage to his shoulder area, Boober said. The bullet is still in the shoulder area and it is not clear if it will be removed, Boober said.
Fletcher was in serious condition Tuesday night, a hospital spokeswoman said.
Boober said Fletcher was conscious Tuesday and somewhat alert. Fletcher, who is also active in the Citizens Fire Co. in Charles Town, was able to make "minor expressions" like a small smile, Boober said.
Many officers and others have traveled to the hospital to visit Fletcher, including a group that went there with Harpers Ferry Police Chief Donald Buracker Monday night. Buracker said Cpl. Brian Dolan of the Harpers Ferry Police Department, Ranson Police officer Pat Norris, Shepherdstown Police officer Terry Bellamy and Charles Town Police officer Bill Carper went with him.
When they arrived, Pat Smith, Dave Colbert, Mike Dodson and Chris Tennant - all sheriff's department officers - were there, Buracker said.
Fletcher was in the intensive care unit and two people at a time could visit him, Buracker said.
"He's hanging in there. He's being tough," Buracker said Tuesday afternoon.