Weiss scored with 9.1 seconds left in overtime to give Florida a 4-3 win over 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 last 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 straight time with a power-play goal midway through the second period.
Michal Repik scored in his NHL debut earlier in the period to tie it at 2, and Nick Boynton drew the Panthers even at 1 with his third goal 11:26 into the first.
"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 after gave us a lot of jump."
Dany Heatley and Jason Spezza scored in the second for Ottawa. Chris Kelly opened the scoring 7:31 in.
"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 last 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, who was called up from Rochester of the AHL earlier in the day along with forward Tanner Glass, drove the crease and put away Auld's rebound of Keith Ballard's shot from the left corner.
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 in Saturday's 3-2 win over Pittsburgh, put Ottawa ahead 3-2 with his seventh goal in six games - his 12th of the season - at 8:20.
Ottawa defenseman Anton Volchenkov was given a boarding minor with 2:29 remaining in the third for his hit from behind on Panthers right wing Brett McLean.
|Chris Kelly (2) ASST: Nick Foligno (3), Jesse Winchester (4)|
1 - 0 OTT
|Nick Boynton (3) ASST: Ville Peltonen (6), Gregory Campbell (7)|
1 - 1 Tie
|Dany Heatley (14) ASST: NONE|
2 - 1 OTT
|Michal Repik (1) ASST: Keith Ballard (9)|
2 - 2 Tie
|Jason Spezza (12) ASST: Daniel Alfredsson (18)|
3 - 2 OTT
|PPG - Jay Bouwmeester (4) ASST: NONE|
3 - 3 Tie
|Stephen Weiss (4) ASST: Michael Frolik (5)|
4 - 3 FLA
|Power Play %||22.1%||21.2%|
|% on Road||10.0%||32.0%|
|% at Home||29.8%||14.6%|
|Tanner Glass Hi-sticking against Jason Smith|
|Chris Neil Fighting (maj) against Tanner Glass|
|Tanner Glass Fighting (maj) against Chris Neil|
|Daniel Alfredsson Interference on goalkeeper against Craig Anderson|
|Alexandre Picard Hooking against Kamil Kreps|
|Jassen Cullimore Interference against Shean Donovan|
|Radek Dvorak Hooking against Mike Fisher|
|Chris Neil Hi-sticking against Brett McLean|
|Anton Volchenkov Hooking against Radek Dvorak|
|Anton Volchenkov Boarding against Brett McLean|