The Detroit News/WDIV-TV poll found 39.6 percent of respondents supporting Peters to 35.3 percent for Land, with 23 percent saying they have not made up their minds. Peters' 4.3 percent lead was just slightly larger than the poll's margin of error.
Peters and Land are contesting the seat left vacant by the retirement of Carl Levin, who, with six terms under his belt, is one of the most senior Democrats in the Senate.
Republican Gov. Rick Snyder was 10 percentage points ahead of former U.S. Rep. Mark Schauer. The poll gave Snyder 45 percent of the vote to 35.2 percent for Schauer and 18 percent undecided.
Pollster Richard Czuba, the president of the Glengariff Group and an official under former Republican Gov. John Engler, said Schauer's big problem is lack of name recognition. He said many Democrats either do not know who he is or say they have no attitude toward him.
"That's a big problem for a candidate five months out and your base doesn't know who you are yet," Czuba told the News.
But Zack Pohl, a spokesman for the Schauer campaign, said the numbers also suggest Snyder has problems.
"For a Republican pollster to have a universally known Republican governor stuck below 50 percent just shows that he's in serious trouble," Pohl said. "That's the danger sign for any incumbent to be stuck below 50 percent."
Glengariff surveyed 600 likely voters between May 20 and May 22.