Weber gave the Predators a brief 1-0 lead when he skated in from the left point and beat Florida goaltender Craig Anderson to his stick side at 16:29 on the power play.
Florida tied it at 17:32 when Olesz skated in on a short breakaway beating goalie Pekka Rinne low to the stick side.
Skrastins gave Florida a 2-1 lead at 11:15 of the second period when his one-timer from the middle of the slot went over Rinne’s left shoulder.
The Predators were held scoreless in the second period on nine shots.
At 9:51 of the third period Anderson blocked a shot by David Legwand. Erat skated in and put in the rebound to tie it 2-2.
Rinne turned back all 10 shots in the third period.
The Predators spent two minutes on the power play in overtime, but were not able to beat Anderson. The Predators outshot Florida 3-2 in overtime.
Ryan Suter has assists in four straight games for the Predators. … Florida’s Nathan Horton played in his 300th career NHL game, and Olesz played in his 200th. … Florida began a five-game road trip. … The Predators will play their next six on the road. … It was the first shootout of the season for the Panthers and the third for the Predators, who are 2-1.