A former Republican county chairman also won his party's primary runoff in a central Mississippi congressional district, beating a one-time state senator.
Rain in many parts of the state kept turnout light in the follow-up to March 11 general primaries, officials said.
Southaven Mayor Greg Davis and Travis Childers, the Prentiss County chancery clerk, will get little reprieve from campaigning in the northern 1st Congressional District because they'll compete April 22 in a special election.
The winner will serve the rest of this year to finish the two-year House term that Republican Roger Wicker started in January 2007. Gov. Haley Barbour appointed Wicker to the U.S. Senate in December after Trent Lott resigned.
The 1st District includes fast-growing DeSoto County and the northern cities of Oxford, Tupelo, Columbus and Booneville. Wicker was elected to the congressional seat in 1994.
Childers defeated state Rep. Steve Holland in the Democratic contest.
With 100 percent of precincts reporting, Childers had 20,729 votes, or 57 percent; Holland had 15,439, or 43 percent.
"If I am fortunate enough to be elected, I will lead north Mississippi and represent working north Mississippians like they deserve to be represented," Childers said.
For the Republicans, Davis defeated former Tupelo Mayor Glenn McCullough Jr.
With 100 percent of precincts reporting in the 1st District GOP contest, Davis had 16,830, or 51 percent; McCullough had 16,305, or 49 percent.
Davis said from his election-night party in DeSoto County: "We stand for the strong conservative principles that the 1st District deserves to have representing them in Washington. We feel that is a message that will be well received among all the voters."
In the central 3rd Congressional District race, Gregg Harper, former Rankin County GOP chairman, defeated Charlie Ross, a former state senator who ran unsuccessfully for lieutenant governor in 2007.
Harper will face Democrat Joel Gill, a cattle buyer and seller and an alderman in the tiny Delta town of Pickens, which is not even in the 3rd District. The law does not require candidates to live in the congressional district where they're running - but voters usually expect it.
The 3rd District stretches from Natchez in the southwestern corner of the state to the Jackson suburbs in central Mississippi and to Starkville in the Golden Triangle. It is drawn to favor Republicans.
The general election winner will succeed Republican Rep. Chip Pickering, who was first elected in 1996 and chose not to run this year.
"We're not taking anything for granted," Harper said from his victory party Tuesday night in Jackson. "We're going to work hard. What we did, we didn't do by ourselves to get the nomination. We had the best group of volunteers I've seen in the 30 years I've been involved in politics."