Blake quickly erased the Rangers' only lead of the night in the first period and then scored two power-play goals in the second for his fourth NHL hat trick as the Islanders took a big lead. He already has 19 goals, nine shy of his career best set last season.
Alexei Yashin also scored in the middle frame for the Islanders, who won for the third time in four games and earned their second road victory of the season over the Rangers. Rick DiPietro gave up two goals to Jaromir Jagr to let the Rangers get close, but finished with 30 saves to win for the fifth time in seven decisions.
The Rangers are injured, sick, and spiralling on the heels of their best stretch this season. They extended their season-high winning streak to five with a 5-2 victory at Dallas last Thursday, but have dropped three straight since - tying their worst run - and been outscored 19-6.
Brendan Shanahan and Jagr, presented with silver sticks before the game in honour of their 600th NHL goals this season, both added to their totals for the Rangers, who played their eighth game in 13 days. Jagr scored the final two and made it 4-3 with 8:15 left.
It wasn't enough to help backup goalie Kevin Weekes, forced into action for the fifth time in six games because Henrik Lundqvist called in sick just hours before the opening faceoff. Weekes has allowed 10 goals on 54 shots in two games.
After a 9-2 loss at Toronto on Saturday and a 6-1 home defeat against New Jersey a day later, the Rangers took an early lead.
Shanahan needed just 18 seconds of Tom Poti's tripping penalty to give the Rangers a 1-0 advantage at 8:58 - New York's first power-play goal in 11 chances over three games.
But Blake intercepted Jagr's behind-the-back pass in the neutral zone, cut across the Rangers' end and wristed a shot past Weekes to tie it 43 seconds later.
The Rangers fell into their undisciplined ways in the second period and were short-handed for much of the first half.
Shanahan took a roughing penalty when he punched Brendan Witt in the face after a stoppage, and Jagr followed him into the box 25 seconds later to give the Islanders a 5-on-3 advantage.
Blake made it hurt when his pass to Yashin hit the stick of Rangers defenceman Aaron Ward and slid past Weekes at 5:53. Darius Kasparaitis went off for hooking at 6:54, putting the Rangers down two men again.
Blake struck at 7:45, taking Miroslav Satan's blind pass and ripping a shot from the right circle. That left Rangers coach Tom Renney shaking his head and muttering on the bench.
Yashin made it 4-1 at 12:31. Jagr cut the Rangers' deficit in half during a power play in the final minute of the period.
Notes: Shanahan's longtime Detroit teammate Steve Yzerman and Jagr's former Pittsburgh linemate Mario Lemieux - also members of the 600-goal club - were surprise on-ice guests. ... The Rangers were also without C Matt Cullen (knee), C Michael Nylander (flu) and D Marek Malik (groin). G Al Montoya, RW Ryan Callahan and D Thomas Pock were recalled from AHL Hartford. ... Blake had an eight-game point streak snapped in the Islanders' 7-4 win over the Rangers on Dec. 3. ... Shanahan and Martin Straka had two assists each, Jagr one.