DiPietro extended his home shutout streak to 185:43. The last goal he allowed at Nassau Coliseum came with 43 seconds left in regulation of a 2-1 shootout win against Florida on Dec. 9.
The Islanders moved one point ahead of the Rangers, just behind the Atlantic Division-leading New Jersey Devils. The Islanders also have three games in hand on the Rangers, who have lost six straight overall following a five-game winning streak.
Henrik Lundqvist was strong in goal for the Rangers, turning aside 36 shots.
The Islanders came out hitting and took six of the first seven shots in the scoreless first period, which featured 7:05 of uninterrupted action.
The Rangers had a great opportunity to take the lead at 7:40 when Adam Hall had DiPietro down as he crossed the net from left to right, but the goalie stuck out his left pad and just got a piece of the puck on Hall's shot.
DiPietro stayed sharp at the start of the second period, making a rising glove save on Jason Ward's turnaround shot 30 seconds in.
Asham put the Islanders in front at 16:43 with his sixth goal of the season. He took a pass from Richard Park at the red line, sped into the slot and fired a 45-foot slap shot that hit defenceman Karel Rachunek's stick and got past Lundqvist under his left arm.
The Islanders made it 2-0 shortly after a power play expired early in the third. With sustained pressure in the Rangers zone, Blake took former Ranger Tom Poti's cross-ice pass and wristed a shot from the left circle over Lundqvist's glove for his team-leading 21st goal at 1:48.