Gudus got control of the puck in the right circle and launched a slap shot that eluded the glove of Hurricanes goalie Justin Peters for the decisive goal, as the Bolts improved to 14-3-1 on home ice with a fourth straight victory overall.
Martin St. Louis erased a 2-1 deficit with a with a power-play goal in the third period and Victor Hedman scored for the Lightning, which downed Carolina for the sixth time in seven meetings.
Ben Bishop made 25 saves.
Peters stopped 47 shots for the Hurricanes, who fell for the fifth time in six games overall.
Jiri Tlusty scored both Carolina goals.