The captain was hospitalized with cuts and a leg injury, while the tech sergeant had no apparent injuries, and both men are expected to be fine.
A Thunderbirds statement said the F-16D Fighting Falcon was conducting a "single-ship familiarization" when it had the "mishap".
Dayton is about 55 miles (89 kilometers) north of Cincinnati.
According to a feature article on the United States Air Force Thunderbirds website, Gonsalves is an advanced pilot and narrator with the Thunderbirds.
"They were very courageous throughout, and they assisted in their own recovery", Heard said of the two team members.More news: Meet Martha, the big, lazy, gassy winner of World's Ugliest Dog Contest
He says the Thunderbirds have decided not to fly in Saturday's show.
"If I can't ensure team safety and crowd safety, we won't fly", he said. Reed says there was no immediate report of any injuries.
The 43rd annual show will include a U.S. Navy F/A-18 Super Hornet, an F-35 Lightning II and the Misty Blues All Woman Skydiving Team. The passenger, Sgt. Kenneth Cordova of Littleton, was rescued about 20 minutes later.
Several emergency crews are responding to a military plane accident at Dayton International Airport. The jet ended up upside down off the runway. "Both teammates were extremely fearless during the extraction and we'd like to thank Wright-Patterson Crash and Recovery, Dayton International Fire Rescue, local police, medical personnel and team members on scene for their incredible recovery efforts".