The Dakota Hills Complex fire consists of three fires burning in brush and ponderosa pines.
Park spokesman David Eaker said the winds forced helicopters to carry out about 30 firefighters battling two smaller fires in a rugged region of the park that have charred more than 200 acres each.
Eaker said smoke jumpers fighting the largest of the three fires, which has blackened more than 1,200 acres, pulled back to a safety zone today.
Eaker said the winds, fanning the flames north and east, were expected as part of the red-flag warning issued for southwestern Utah.
A new management team from Arizona is expected to be in place Thursday to take over fighting the fire that started with a lightning strike on Sunday and leapt to life on Monday.
Several popular hiking trails remain closed, and Eaker said park visitors are cooperating.
Besides the fire crews, the flames are being doused from the air by a heavy-lift helicopter. Single-engine air tankers are dropping retardant.
In northern Utah, crews were getting the upper hand on two fires northeast of Grouse Creek in northwestern Box Elder County.
Bureau of Land Management spokeswoman Teresa Rigby said the Beke fire, started by lightning July 16, has burned more than 1,000 acres and is about 80 percent contained.
She said thunder cells that passed over the region on Tuesday breathed new life into the fire, which grew about 300 acres. But fire crews responded and stopped the advance - with the help of rain also brought in by the storms.
The fire is being fought by about 20 firefighters, a single-engine air tanker and several fire engines.
The Pine Creek fire - it was started by lightning July 15 - is about 95 percent contained after burning 140 acres, said Rigby. It is being fought with about 20 firefighters and a one fire engine.
Both fires are expected to be contained sometime later today, said Rigby.