Greiss, who has four shutouts this season and 12 in the NHL, is 4-0-1 with a .987 save percentage in his past five games.
"Sometimes you're lucky, the puck bounces your way," Greiss said. "You've got to take it, hopefully go as long as you] can.
"The boys made me look good out there, they're battling hard, a lot of blocked shots, not many rebounds."
***[WATCH: [All Islanders vs. Blue Jackets highlights]*
Casey Cizikas scored twice, and Josh Bailey had a goal and an assist for the Islanders (34-17-6), who have won four of their past five games and are 10-2-2 in their past 14.
"We made plays when they were there. (It was) a full 60 (minute) effort," Cizikas said.
Sergei Bobrovsky made 24 saves for the Blue Jackets (32-21-3), who had won four in a row.
"Give them credit. They have the No. 1 defensive team for a reason," Blue Jackets coach John Tortorella said. "Early on, both teams played in spurts. They scored when they had chances. We had chances and didn't score."
Cizikas made it 1-0 at 7:06 of the first period on a breakaway. Cal Clutterbuck started the breakout by taking an outlet pass from Greiss before sending a stretch pass to Cizikas, who deked Bobrovsky and finished with a backhand.