The pair finished the day at 11-under 202, one stroke ahead of the rest of the field.
Goosen won the Transitions event in 2009. Furyk was the 2010 champion.
Sang-Moon Bae held the lead until stumbling to a triple-bogey at the par-five 16th. He bounced back with a birdie on 17, ending the day with a 3-under 68, good for a second-place tie.
Second-round leader Jason Dufner joined him at minus-10 with an even-par 71.