The (Sioux Falls) Argus Leader reported that with 582 of 710 precincts reporting, Varilek had 72.44 percent of the vote to 27.56 percent for Jeff Barth, a retired telephone company technician and county commissioner.
Varilek will go up against Republican incumbent Kristi Noem, who is seeking a second term.
In the state's GOP presidential primary, presumptive party nominee Mitt Romney picked up the lion's share of the 23 delegates at stake. Romney had 66.05 percent of the vote to 12.7 percent for U.S. Rep. Ron Paul of Texas, 11.71 percent for former U.S. Sen. Rick Santorum of Pennsylvania, 5.47 percent uncommitted and 4.05 percent for former U.S. House Speaker Newt Gingrich of Georgia.
Romney already had surpassed the 1,144 delegates he needed to secure the party's nomination heading into Tuesday's voting in South Dakota and six other states.