Mike York, Viktor Kozlov, Mike Sillinger and Jason Blake also scored for the Islanders, who went 4-1-2 on their seven-game homestand. After visiting New Jersey on Thursday, New York will play two more games at home before a five-game road trip.
Jassen Cullimore and Denis Arkhipov scored for the Blackhawks, who snapped a three-game shutout streak but lost their sixth straight game. Chicago hasn't won since a 2-1 home victory over Montreal on Oct. 18. Brian Boucher stopped 19 shots but fell to 0-6.
Cullimore's goal with 4:14 left in the second period was the Blackhawks' first in 240 minutes, 56 seconds - dating to a score by Michal Handzus on Oct. 21 in a 4-3 home loss to St. Louis.
The Blackhawks outshot the Islanders 10-8 in the opening period, but New York had the better chances. The Islanders took advantage of their third power play with 1:41 left in the period when York knocked in the rebound of Miroslav Satan's right point slap shot for his third goal of the season.
In the second period, three straight Islanders penalties gave Chicago a pair of two-man advantages that lasted 19 and 48 seconds. DiPietro stopped six shots in that span to preserve the 1-0 lead.
New York made it 2-0 at 11:44 when Kozlov picked off a pass at his own blue-line and sped in alone on Boucher. He faked a forehand move, switched to his backhand, and slid the puck into the open left side.
Yashin extended the lead to 3-0 at 14:38 on a power-play slap shot from outside the left circle that beat Boucher - who was screened - between the pads. The Islanders captain has three goals and six assists in his last five games.
Cullimore ended the Blackhawks' scoring drought when his shot from the right point deflected off Islanders defenceman Alexei Zhitnik and over DiPietro's glove into the top left corner.
Chicago scored again 82 seconds into the final period. Arkhipov picked up a loose puck at his own blue-line, skated to the high slot and beat DiPietro with a wrist shot to the right side.
Sillinger iced the game with 2:30 left on a wrist shot from the low right side that got between Boucher's pads. Blake scored his 100th NHL goal on a power play from the right crease with 52.7 seconds remaining.
Notes: After Handzus' goal against St. Louis, Chicago was shut out at home by Vancouver (5-0) and Anaheim (3-0), and then Monday night in Philadelphia (3-0). . . . Attendance was announced as 8,739, the smallest crowd of the season in the Islanders' seven home games.