The Islanders failed in their bid to produce their first three-game winning streak of the season. New York, however, has earned at least one point in six straight outings.
Sharp put back a rebound of a shot by Marian Hossa to give Chicago its third win in four games.
Hossa scored the only goal of the first period and Sharp tallied 2:23 into the second to give the Blackhawks a 2-0 lead. Travis Hamonic got one back for the Islanders late in the second and Steve Staios tied it midway through the third.
The goals for Hamonic and Staios were their first of the season.