Ronning, who signed as a free agent on Jan. 9, beat goaltender Mika Noronen on the power play 3:45 into his 1,100th NHL game for his first goal since April 6.
Less than two minutes later, Jonsson doubled the lead when he scored on a slap shot from the point.
Arron Asham set up second-period goals by Dave Scatchard and Niinimaa to stretch the Islanders' lead to 4-1.
Chris Taylor and James Patrick scored for the Sabres, who have just two wins in their last 13 road games (2-10-1).
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