Chris Phillips also scored for Ottawa, and Craig Anderson made 25 saves. Jason Spezza added an empty-net goal with 1:16 remaining.
Tomas Fleischmann scored and Jose Theodore stopped 34 of 36 shots for Florida. The defending Southeast Division champions fell to 1-3.
Ottawa has won 11 of the last 12 meetings between the teams.
Theodore stopped Guillaume Latendresse on a penalty shot with 9:11 left in the third period. Brian Campbell was called for hooking Latendresse as the Senators player skated in on goal.
Karlsson scored his second goal to give Ottawa the lead 8:28 into the second period. He intercepted Shawn Matthias' cross-ice pass in the neutral zone, skated in on the left side and wristed a right-handed shot past Theodore high to the stick side.
Fleischmann and Phillips both scored power-play goals to leave the score tied at 1 after one period.
NOTES: Florida C Stephen Weiss (lower body) did not dress. . Ottawa concludes its two-game road trip in Florida at Tampa Bay on Friday night. The Senators then have a three-game homestand (Pittsburgh, Washington, Montreal). ... Philadelphia visits Florida on Saturday night. . The Panthers' only win in their last 12 games against Ottawa came at home on March 4, 2012.