The 33-year-old entered the final round with a three-shot advantage and remained in front for most of the day. However, with several chasers going low - including Kisner - Streb saw his solo lead vanish after a bogey on No. 13, which was his first blemish since Thursday.
Streb then three-putted for par on the par-5 15th to remain one behind Kisner but found a birdie on No. 17 to pull even with the clubhouse leader at 19-under.
On the first playoff hole, Streb scrambled for par while Kisner missed a 14-foot birdie effort that would have secured the victory. The Oklahoma native then hit the shot of the tournament on the second extra hole, stuffing his approach shot from 159 yards - that nearly went in for eagle - to 15 inches for a tap-in birdie.
Kisner couldn't chip in, giving Streb his first win since 2014. He also becomes the first two-time winner of the RSM Classic.
"It's nice to get another one knocked off," Streb said about his long-awaited second victory. "Obviously Kiz played a great round today and I just snuck one in there on 17. Felt pretty fortunate to get in the playoff the way things were kind of running there at the end, so really nice to get another one."
Streb moves from outside the top 350 in the world to No. 116 with his $1.188-million payday.
Here's how the top of the leaderboard finished from St. Simons Island, Georgia:
|Place||Player||To Par||R4 Score|
* Denotes playoff victory.
Kisner, who fired 63 to force extra holes, dropped his career playoff record to 0-5.
The PGA Tour is off next week before returning for the Mayakoba Golf Classic in Mexico on Dec. 3.