Nick Leddy and John Tavares scored for New York (4-2-0), which lost its second game in a row Jaroslav Halak allowed five goals on 23 shots before being replaced by Chad Johnson at the start of the third period.
Johnson stopped all five shots he faced.
"We were just easy to play against," Tavares said. "We were just soft on pucks, we stopped moving our feet, and we were just an easy team to play against."
Toronto turned a 2-1 deficit at the start of the second period into 5-2 advantage by intermission, as the Leafs peppered Halak for four goals on 13 shots.
Kessel started the offensive onslaught at 9:04 of the second with his third of the season which tied the game 2-2.
Polak gave Toronto its first lead of the game 2:07 after Kessel's goal with his first as a Leaf. Santorelli and Daniel Winnik set up the go-ahead goal by controlling the puck behind the goal line before Polak scored his 14th career goal in 431 games.
Clarkson pushed the advantage to 4-2 with 3:39 remaining in the period with a snap shot from the high slot that Halak couldn't glove. Kessel scored his second of the period 92 seconds later causing the 11,408 in attendance to boo the Islanders off the ice.
"In (the) second we got back to working," Clarkson said. "(We) took the puck in their zone and started cycling, making plays. We were better in our own zone. The difference in the game was the second.
"We'll take the positives from that."
As dominant as Toronto was in the second period, the Islanders were their equals in the opening 20 minutes.
Leddy opened the scoring just 2:48 into the game as he walked down the slot before beating Bernier with a wrist shot.
Van Riemsdyk equalized nearly six minutes later. New York defenseman Thomas Hickey lost the puck in the corner, and Kessel found van Riemsdyk alone in the slot for his third goal of the season.
But the Islanders went ahead 2-1 on Tavares' power play goal at 15:02. The New York center one-timed the rebound of Johnny Boychuk's point shot, which had ricocheted off the backboard, past Bernier.
"We knew the early history of the season with their hockey club, they really come at you in the early going," Leafs coach Randy Carlyle said. "We weathered a storm. They score the first goal, we get it back. They score the second goal, we get it back. After that we kind of got things going our way in the second period
NOTES: The Islanders will introduce their new owners, Jonathan Ledecky and Scott Malkin, in a press conference Wednesday afternoon at the Nassau Coliseum. Ledecky and Malkin will spend the 2014-15 and 2015-16 seasons as the franchise's minority owners, then transitioning into the majority owners starting in 2016-17. ... Toronto announced the hiring of Mark Hunter as the Director of Player Personnel in a statement Tuesday morning. "I am very excited about joining the Toronto Maple Leafs organization," said Hunter, who stepped down from his role as owner, Vice President and General Manager of the Ontario Hockey League's London Knights to take the position with the Leafs. "I am grateful for the opportunity that has been given to me by (Maple Leafs President) Brendan Shanahan, (General Manager) David Nonis and the entire management team. I would like to thank the London Knights organization for 12 great years. I am looking forward to the start of a new chapter in Toronto."