Tavares had two goals and an assist Thursday as the seventh-place Islanders rallied past Toronto 5-3 on Thursday and moved within two points of the Maple Leafs for fifth place in the Eastern Conference.
The Islanders overcame an early 2-0 deficit to win the first of five straight road games they will play to end the regular season. They improved to 13-5-2 away from home, and earned their fifth win in six games as they chase their first playoff berth since 2007.
"That's where we want to go, we want to keep moving up ... and take care of our own business," Tavares said. "That's the best way to handle the situation we're in.
"We know when we play well we can really take advantage of our opportunity here and not just get in but keep playing."
New York is 10-1-2 in its last 13 games.
"We've still got 12 periods of hockey left and on the road against some good quality teams," Tavares said.
Toronto will have to wait to clinch its first playoff berth since 2004. The Leafs could have ended their postseason drought with a win over the Islanders and a Carolina victory over the Winnipeg Jets, but instead dropped to 13-8-2 at home with a second straight loss.
Now the Leafs head into an important road game in Ottawa against the sixth-place Senators.
Franson said Toronto's woes aren't the result of the club looking ahead to the postseason.
"We have to stop the bleeding here and get back to what made us successful," he said. "But our lack of lack of success the last two games has nothing to do with thinking we've got a playoff spot.
"This is adversity. A lot of our mistakes are usually correctable, we just have to pay attention."
Lupul said after going ahead, the Leafs became their own worst enemy.
"We were making awful, awful turnovers especially when we got up 2-0 in the first," he said. "We were throwing the puck in the middle of the ice and giving them a chance to turn the momentum and have success.
The Islanders controlled an eventful first, outshooting Toronto 19-5 but needed a late surge to erase a 2-0 deficit. Moulson's power-play goal, his 15th, at 15:03 tied it before Tavares gave New York a 3-2 lead at 17:24.
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.
Lupul opened the scoring at 5:05, skating around Islanders defenseman Matt Carkner and putting a shot through goalie Evgeni Nabokov'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.
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.