Hemsky moved in and fired a shot off the post and into the back of the net behind goaltender Cam Ward to give the Senators their third straight win, and fourth in their past fifth games.
Mika Zibanejad scored in regulation for the Senators (32-29-14) while Anderson made 30 saves.
Jeff Skinner had the Carolina goal while Ward backstopped the Hurricanes (32-32-11) through regulation with 28 saves.
Coincidental minor penalties in overtime meant the teams played two minutes of three-on-three hockey. Kyle Turris had the best opportunity for the Senators during that span but his shot went over the net. Alex Semin had Anderson beat on a two-on-one but his backhand went wide.
There was very little in the way of scoring opportunities through most of the third period. That changed in the final few minutes as both teams started to apply pressure as neither wanted the other to claim a bonus point in the tight playoff race.
As it stands now, the Senators are four points behind the Columbus Blue Jackets, who currently possess the second wild-card berth with 82 points. The Hurricanes are seven back.
The way the first period started it seemed as though the goaltenders were going to have nightmares even before they went to bed.
The score was tied 1-1 before the five-minute mark and the non-defensive style was allowing for several opportunities on both sides.
Zibanejad opened the scoring at 1:41 of the first period when he deflected a Patrick Wiercioch point shot past Ward. The play was reviewed but quickly announced that the call on the ice stood and it was in fact a goal.
Zibanejad continues to improve on his career-high numbers as he now has 14 goals and 29 points in 64 games.
It wasn't all good news for the Senators though as Erik Karlsson gave the puck away behind his own goal and then was the last player to touch it before it went into the back of the Ottawa goal behind Anderson.
Karlsson tried to sweep the puck around the boards behind the net but fanned on his attempt, giving skinner possession of the puck behind the goal.
He danced from side-to-side before banking the puck off Karlsson and in to tie the game at the 4:03 mark.
Notes— Jason Spezza, Bobby Ryan, Jared Cowen and Colin Greening were scratches for the Senators. Mike Komisarek, Radek Dvorak and Justin Peters were scratches for the Hurricanes…The Senators recalled Jean-Gabriel Pageau from Binghamton on Monday…Senators forward Kyle Turris was named the NHL's First Star of the Week Monday after collecting four goals and three assists in four games…Jeff Skinner now has points in five straight games and recorded his 30th goal of the season Monday…The Carolina Hurricanes are scheduled to play back-to-back games 20 times this season, second only to the 22 of the New Jersey Devils…nine of the past 11 games between the Senators and Hurricanes have been decided by one goal.