They weren't aware that Salt River Project was releasing water from the Horseshoe Dam, and the water became too much for them.
Two adults and two young children clung to trees in the middle of the river after their boat capsized.
The call for help came into the Maricopa County Sheriff's Office and the Department of Public Safety around 9 p.m. Monday. The family of four was unaware of the water release and found themselves in serious trouble.
"When the flow increased, they lost control, they washed into a tree or strainer, and they were able to hold on to some of the trees in the wash," said Spencer Smith with MCSO's Mountain Rescue unit.
Smith and other members of the team prepared and planned to paddle out to the family in rafts. DPS sent a helicopter that hovered to provide light and a backup rescue if anyone was swept down the river.
Officer-Paramedic Eric Tarr was in the helicopter over the scene and described what happened. "And there's the second child in the boat... you're going to see them paddle off, and you're going to see them paddle off into the shore," said Eric Tarr.
"The children were actually in higher spirits than they thought they would be, because the water was extremely cold, and it was rising, they were in a very dangerous situation, but their father was there to keep them calm as well," said Tarr.
Once the kids were safely on the bank, the rescue team went back and got both adults.
Tarr described the rescue as precise and smooth.
"It's always a relief for them, and for us to get everybody safely out of the water. I'm not aware of any other injuries other than being cold and wet, they are very fortunate," he said.
To volunteer or donate to the MCSO Mountain Rescue unit visit http://www.mountainrescue.org/