Chafee -- whose father was Rhode Island's governor from 1963-1969 -- had 36 percent of the vote compared with Robitaille's 34 percent, unofficial results indicated.
"Rhode Island has elected its first independent governor," the former U.S. senator, who left the Republican Party in 2007, said in his victory speech.
Chafee congratulated Democratic Providence Mayor David Cicilline for his 1st Congressional District win in northern and eastern Rhode Island and Democratic U.S. Rep. James R. Langevin, who won re-election in the state's 2nd Congressional District in the southern and western part of the state.
"I am very grateful to all the Rhode Island people who've given me your vote," The Providence Journal quoted Chafee as saying.
"And I give you my word. I will always be honest with you. I will always do what is right for Rhode Island."
Democrat A. Ralph Mollis won re-election as Rhode Island's Secretary of State, narrowly defeating Republican Catherine Taylor.