Chief Ed Porter Jr. of Gaston Fire and Rescue said in a statement the call was received shortly before 1:15 p.m.
Gaston sent two swiftwater teams to the boat landing at River Falls Park. Roanoke Valley Rescue Squad arrived for backup, said Weldon Fire Department Chief Rusty Bolt, who was also at the scene.
The swiftwater team found two men holding onto the overturned boat, Porter said in the statement.
Bolt said the dog was on top of the boat.
They were found about a mile down river from the landing, Porter said.
The victims and the dog were pulled aboard the Gaston boat. The men refused medical treatment and left the scene.
Weldon recovered the boat, which Bolt said had Virginia registration.
Porter said bystanders reported the men attempted to shoot a gap at the river when the boat overturned.
North Carolina Wildlife Resources Commission Officer Patrick Brown said the boat capsized as the operators were trying to navigate the river between rocks and the water was too shallow, causing the boat to overturn. Brown said the swift currents also factored in the boat capsizing.
No violations were detected.
First responders cleared the scene shortly after 2 p.m.