Tavares fired a shot on a 2-on-1 break that Leafs goalie James Reimer got a piece of but couldn't keep out for his 25th goal of the season.
Boyes had earlier converted Tavares' smart centering pass for his ninth goal at 9:07 that cut Toronto's lead to 2-1.
"I think we've got some guys in here that have matured over the years," head coach Jack Capuano said. "We have a young team. I think guys like (Evgeni) Nabokov and Brad Boyes, guys that have been there before, have been vocal and really good for us."
Lupul opened the scoring at 5:05, skating around Islanders defenseman Matt Carkner and putting a shot through Nabakov's legs for his ninth of the season. It came after Toronto, which boasts the NHL's third-ranked penalty-kill unit, successfully defended a two-man New York power play for 1:28 early in the period, with Reimer making a nice save off Moulson.
Franson's power-play goal at 6:41, his fourth this season, gave the Leafs a 2-0 advantage as they scored on their first two shots of the period.
It was more of the same in the second as the Islanders held a 15-5 edge in shots and had the period's lone goal. Tavares scored his second of the game and 26th overall at 14:40.
Nielsen made it 5-2 with his fifth goal at 10:22 of the third before Phaneuf rounded out the scoring late on the power play.
"It seems at times we're trying to do too much as individuals and it's costing us," Leafs coach Randy Carlyle said.
Notes: Toronto and Buffalo are tied for the NHL's youngest roster with an average age of 26.9 years of age. ... The Islanders came in sporting a 20-2-2 record when they score at least three goals but just 2-14-3 when scoring two or fewer times. ... New York defenseman Andrew MacDonald entered Thursday's action with a league-high 114 blocked shots.