The goal spared Vancouver's blushes after they had let a 2-0 lead, given to them by Chris Higgins and Kesler, slip.
Scores from Alexander Steen at the end of the second period and Vladimir Sobotka in the third helped the Blues force OT, but Kesler sealed the win for Vancouver, their third in a row and fifth from a gruelling seven-game road trip.
Josh Bailey scored with 1:40 left to play as the New York Islanders rallied for a 4-3 win over the Pittsburgh Penguins.
Trailing 2-1 going into the third, Frans Nielsen levelled at 12:46, but Deryk Engelland put Pittsburgh back ahead just 16 seconds later.
That lead lasted less than a minute before Pierre-Marc Bouchard scored, then Bailey settled it in the closing moments.
Marian Gaborik netted the go-ahead goal in the third as the Columbus Blue Jackets stretched their winning run to three by beating the Toronto Maple Leafs 5-2.
Elsehwere the Buffalo Sabres halted a three-game skid by beating the Florida Panthers 3-1, the Anaheim Ducks edged out the Ottawa Senators 2-1 and the Colorado Avalanche were 4-2 winners over the Carolina Hurricanes.