Lynch, 58, won most of the state, including Stephen's home ward.
"Our state faces challenges over the next two years," Lynch said in his victory speech. "But with good New Hampshire common sense, hard work and cooperation, we will conquer those challenges."
Stephen, 48, who lost in his third bid for elective office, promised to cut spending without raising taxes.
Despite the easy win for Lynch, Democrats lost control of the state legislature, known as the General Court of New Hampshire, in Tuesday's vote.
In the U.S. Senate race, Republican Kelly Ayotte defeated Democratic Rep. Paul Hodes.
Ayotte tallied 61 percent of the vote to Hodes' 38 percent, with 82 percent of the vote counted. Independent Chris Booth got 2 percent of the vote while Liberal Ken Blevens got 1 percent.
Ayotte will take the seat currently held by Republican Judd Gregg, who did not seek re-election. Gregg, a former New Hampshire governor, is the ranking member of the Senate Budget Committee.
Jennifer Lawrence: 'It should be illegal to call somebody fat on TV'
Abigail Breslin wears sheer paneled gown for 'August: Osage County' premiere