The stars were surrounded by police and security, who fought off photographers trying to snap final pics of the pair.
Kristen and Taylor arrived at the airport at around 6am in a fleet of Escalades, accompanied by up to a dozen minders.
Travellers looked on in horror as photographers were pushed out of the way as the group headed to a private check-in area. At one point, Kristen began running.
Several photographers were injured in the crush. An onlooker said: "It was pretty horrible to witness. It looked like the police and security guards were extremely heavy-handed."
Check out the footage...
Wide World of Sports
Latest celebrity news
Fat Tony & Co
The Big Bang Theory
2 Broke Girls
Two and a Half Men
House & Garden