Weiss scored with 9.1 seconds left in overtime to give Florida a 4-3 victory against Ottawa on Monday night.
The Panthers' center drove a shot from just over the blue line past Alex Auld as Florida improved to 5-1-2 in its past eight games.
"To be honest with you, I was a little on the tired side there and I was just trying to get it on the net," Weiss said. "It goes in sometimes when you shoot."
Anderson slid across to his right to deny Mike Fisher with a sensational save moments earlier.
"The shootout's a crapshoot, you know, it comes down to individual efforts there," said Anderson, who finished with 34 saves. "We're a team and we like to play as a unit, and the more we can take the individual out of the game, keep (Jason) Spezza and (Dany) Heatley and all of those guys out of the 1-on-1 game, we're better off, so I enjoyed the victory in overtime."
Jay Bouwmeester drew Florida even for the third consecutive time with a power-play goal midway through the second period.
"That shows a lot of character," Weiss said. "This is a tough building to play in. They're a good hockey club, especially when you get down; they're tough to come back on and to get those goals right away gave us a lot of jump."
"Give them credit -- they battled all night," Kelly said. "It is pretty tough to lose that late in the game."
The Senators, 4-1-3 in their past eight games, had a great opportunity to gain the lead for a fourth time late in the second, yet failed to convert on a two-man advantage that lasted the final 1:29 of the middle period.
"We got a point," Fisher said. "We've just got keep building and finding ways to get points, but at the same time, we've got to win games like that."
Kelly opened the scoring when he pushed a loose puck across the goal line while Senators forward Nick Foligno fell into the net. After a video review supported the on-ice call, referee Tom Kowal announced the decision to the crowd, describing it as "a good hockey goal."
"Most times if you know that it might not be a goal, then you kind of worry, but I was pretty confident that there was no reason for it not to be a goal," said Kelly, who didn't hear Kowal's unique announcement. "He didn't have possesion, the net wasn't knocked off, he didn't blow the whistle down, so there really wasn't much worry."
Boynton drew the Panthers even with his third goal at 11:26.
Heatley scored his team-leading 14th goal 2:32 into the second, beating Anderson with a shot from the right side.
Repik skated straight to the Panthers bench to celebrate the goal while Ballard recovered the milestone puck from linesman Derek Amell.
"Obviously, I will keep it," Repik said. "It's my first goal in the National Hockey League. It's my dream. I came to play in the NHL and I scored a goal."
Tanner and Ottawa's Chris Neil got fighting majors one second later when they squared off after lining up for the ensuing faceoff.
Spezza, who recorded a hat trick Saturday in a 3-2 victory against Pittsburgh, put Ottawa ahead 3-2 with his seventh goal in six games -- his 12th of the season -- at 8:20.
- Repik is the fourth rookie, along with C Michael Frolik, LW Kenndal McArdle and D Jason Garrison, to play his first career game with Florida this season.
- Bouwmeester, who ended a five-game points streak Saturday, has 13 points (four goals, nine assists) in his past 13 games.
- Auld, who stopped 36 shots, made his 11th consecutive start.