Bill Guerin and Jordan Staal also scored for the Penguins, who won their third in a row to remain undefeated on the road despite Crosby and Evgeni Malkin being held off the scoresheet.
"He's the best player in the world and you know that's why he gets the publicity," said Kennedy, who had a couple reporters around him while a camera-laden scrum besieged Crosby. "He deserves everything he gets."
Kennedy gave Pittsburgh a 2-1 lead in the second with his third goal of the season. He added his fourth goal -- his second of the game -- later in the period when he beat Pascal Leclaire with a slap shot from the top of the right faceoff circle.
Crosby, who scored twice in a 5-2 win in Toronto on Saturday, praised the work of Kennedy and his linemates, Matt Cooke and Craig Adams.
"He's playing great for us and that whole line has really been great," said Crosby, who was held without a point for the third time in four games. "You could see the chemistry kind of start last season and you see it right off the bat here this season, starting where they left off last year so that's huge for us and we really pride ourselves on our depth and having everyone contribute, and they've just really added to that."
Milan Michalek got his first Ottawa goal to open the scoring 15:59 in.
Leclaire made 24 saves as the Senators (3-2-0) ended a three-game winning streak.
Fleury remained undefeated in five starts.
The Penguins improved to 4-0 on the road, including the first three games of their current four-game trip that concludes Wednesday against the Carolina Hurricanes.
Cheechoo took a pass from linemate Jason Spezza and fed Michalek, who cut across the goalmouth to slip the puck around Fleury.
Guerin evened it at 1 just 39 seconds later. The veteran forward put home his own rebound after his initial shot struck Senators defenseman Chris Phillips' skate and bounced out front off the end boards.
"They're a good team," Spezza said. "They're riding high and you get those bounces when you're going that way."
Kennedy got credit for the go-ahead goal 6:16 into the second when his shot struck Ottawa defenseman Erik Karlsson's skate and went into the right side of the net, just beyond Leclaire's vain attempt to kick the puck away with his left pad.
"He's got a great work ethic and he was in on the forecheck and you get bounces when you work hard like that, so he earned that one," Crosby said. "It was a bit of a goofy one but I'm sure he'll take it."
Kennedy increased the lead to 3-1 when he drove a long slap shot past Leclaire at 18:02.
"I just missed it," Leclaire said. "I don't have a whole lot of excuses about it. That's usually a shot that you have to stop."
Staal made it a three-goal margin with his third goal midway through the third.
Crosby has yet to score a goal in six regular-season games in Ottawa, though he has scored four times in five playoff games at Scotiabank Place. ... Adams assisted on both of Kennedy's goals. ... The Penguins have a 23-4-4 regular season mark overall since Dan Bylsma took over as head coach on Feb. 15. ... Rookie Senators center Peter Regin did not play. He is day to day with an upper body injury that forced him to leave midway through the third period of Saturday's 4-2 win over the Atlanta Thrashers.
Copyright by STATS LLC and The Associated Press
Arena: Canadian Tire Centre Location: Ottawa, Ontario
Referees: Chris Ciamaga, Dan O'Halloran Linesmen: Pierre Champoux, Scott Driscoll
Attendance: 17,014 (92.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Milan Michalek (1)
Assists: Jonathan Cheechoo, Jason Spezza
Bill Guerin (2)
Assists: Chris Kunitz, Mark Eaton
Tyler Kennedy (3)
Assists: Jay McKee, Craig Adams
Tyler Kennedy (4)
Assists: Matt Cooke, Craig Adams