In neighboring Indiana Republican Rep. Steve Buyer defeated fellow GOP Rep. Brian Kerns in a face-off also forced by population changes which reduced that state's congressional delegation by one seat.
In Ohio, Timothy Ryan, 28, won his primary. He will face beleaguered Rep. James A. Traficant, the colorful Democrat who was convicted of bribery last month but decided to run as an independent, in the general election.
Traficant's impact on the Ohio race isn't yet known. He was convicted in April of 10 counts of racketeering, bribery and tax evasion and is to be sentenced June 27. He faces up to 63 years in prison, but will likely get less than 20 years because of federal sentencing guidelines.
The results were seen as early examples of how newly drawn political maps will affect congressional races.
Defeated Rep. Sawyer, 56, blamed his defeat on the new political reality. Sawyer's district and Traficant's old Youngstown district were merged by the Republican-controlled Legislature in January as Ohio lost a congressional seat in the redistricting that follows every census.
"The geography of this district was really wired for a hometown boy," Sawyer said in his concession speech.
Ryan had 28,646 votes, or 41 percent, while Sawyer tallied 19,098, or 28 percent, according to unofficial results. Buyer received 43,791 votes, or 55 percent, while Kerns got 23,844, or 30 percent.
Elsewhere in Ohio, former Dayton mayor Mike Turner trounced newspaper executive Roy Brown to win the GOP nomination for a seat being vacated by Democratic Rep. Tony Hall, who is retiring after 24 years to accept the Bush administration's nomination as a U.S. ambassador to the United Nations. Turner will face Democrat Rick Carne, a former aide to Hall.
Brown moved from the Cincinnati area to Dayton to run and loaned his campaign $1 million. Turner, who had the backing of local and national GOP officials, accused his opponent of trying to buy the election.
Turner ended up with 46,542 votes, or 80 percent, while Brown had 8,287 votes, or 14 percent.
Republicans see the district as an opportunity to increase their edge in the House. Democrats need to gain seven seats this fall to be assured of control.
In the race to succeed retiring Democratic Rep. Tim Roemer of Indiana, Republican Chris Chocola and Democrat Jill Long Thompson won their parties' nominations and will face off in the fall.
In the 3rd District of northeastern Indiana, four-term Republican Rep. Mark Souder defeated Paul Helmke, a former three-term mayor of Fort Wayne who was the GOP's nominee for U.S. Senate in 1998.
Republican Dan Burton, seeking his 11th term in Indiana's 5th District, easily defeated challenger George Thomas Holland, a retiree from Rushville. Katherine Fox Carr of Indianapolis beat three other candidates for the Democratic nomination to challenge Burton this fall.
Democrats currently control the U.S. Senate by one seat while Republicans hold the House by six seats. Thirty four Senate seats and all 435 House seats are up for election in November.