After blowing a 3-0 lead in the third period on Wednesday and losing to Detroit in overtime, the Islanders couldn't hold a 2-1 advantage as Jim Slater's wrist shot beat goalie Mike Dunham on the stick side with 10:23 remaining.
Blake bailed out New York with a breakaway goal 2:19 later, sending the puck from the right circle over the shoulder of goalie Kari Lehtonen. It was his fourth goal in five games.
Trent Hunter's 12th goal, which came on the power play with 3:59 left, made it 4-2. Victor Kozlov scored twice, including an empty-netter.
New York earned three of a possible four points in Atlanta during a seven-day span. The Islanders fell behind 3-0 to the Thrashers in the opening six minutes last Friday but rallied to force overtime.
Atlanta, the Southeast Division leaders, had won three of four and five of seven.
The Islanders had lost five of seven and 11 of 15 to fall into 11th place in the East. New York has earned points in five straight games - four since the all-star break.
New York coach Ted Nolan rested centre Alexei Yashin, who has tendinitis in his right knee, and No. 1 goalie Rick DiPietro, who was knocked out quickly by the Thrashers in the previous meeting after he allowed three goals on five shots.