Kesler's first tally off a feed from Sedin 8:23 into the game put the Canucks ahead 2-0. His second came 20 minutes later on a power play and gave Vancouver a three-goal advantage.
Alexander Edler and Dale Weise also scored as the Canucks won their their fourth straight and ninth in 10 games.
Roberto Luongo stopped 24-of-25 shots to earn the victory.
Colin Greening got Ottawa's only goal and Curtis Anderson stopped 24-of-28 shots for the Senators, who fell to 1-3-2 in their last six games.