Crosby, who now has at least one goal in each of the Penguins’ last eight home games, scored three straight goals for his first natural hat trick in more than five years.
Kunitz had a goal and two assists, Kris Letang added a goal and an assist, and Matt Cullen also scored for the Penguins. The six goals were a season high.
Jean-Gabriel Pageau, Mark Stone, Cody Ceci, Chris Wideman and Dave Dziurzynski scored for the Senators.
The Penguins took a 3-1 first period lead on goals by Cullen, Letang and Kunitz while the Senators countered with a tally by Stone. Ottawa made it 3-2 late in the first period on a goal by Wideman.
The Senators then took a 4-3 lead after Pageau and Ceci scored 24 seconds apart to open the second period. With both teams playing 4-on-4, Pageau tipped in Erik Karlsson’s rebound to pull the visitors within a goal. Less than 30 seconds later, Fleury left Zack Smith’s rebound on the doorstep and Ceci poked it past the netminder to put the Senators up 3:25 into the second.
A pair of power play goals changed the game in the Penguins favor, however.
Less than three minutes later, Crosby tied the game at 4-4 with a wristshot from the left circle past Craig Anderson on the power play, assited by Letang and Evgeni Malkin.
Late in the period Crosby scored another power play goal to give the Penguins the lead when he swatted a beautiful centering pass from Malkin past Anderson.
The Penguins went ahead 6-4 early in the third period when Crosby completed the hat trick with a hustling goal, redirecting a potential Kunitz turnover into the Senators’ net.
Dziurzynski scored to bring Ottawa within one, but Fleury held on to secure the win for the Penguins.
Fleury stopped 18 of 23 shots for Pittsburgh, while Ottawa’s Anderson 38 saves.
The Penguins have won four straight and lost in regulation just once since Jan. 6.
The Penguins play at Florida on Friday.