Romney and Hatch had an easy time of it in Utah, a state where Romney has been popular since he helped turn around the 2002 Winter Olympics in Salt Lake City, and where Hatch has been a U.S. senator since 1977.
Romney, a member of the Church of Jesus Christ of Latter Day Saints, won nearly three-quarters of the vote.
Hatch breezed past Democrat Scott Howell, a former state senator. With 82 percent of the votes counted, Hatch had 66 percent to 30 percent for Howell.
Gov. Gary Herbert was easily re-elected over Democratic challenger Peter Cooke. Herbert had 69 percent of the vote with 82 percent of the ballots counted.
Three of the four House races went to Republicans. The lone Democrat to win was Rep. Jim Matheson, who edged Republican Mia Love by fewer than 3,000 votes, the Salt Lake Tribune said late Tuesday.
Matheson, a member of the conservative "Blue Dog" Democrats, represented District 2 for six terms but opted to run in the new and more-urban District 4. His opponent, the daughter of Haitian immigrants, is the mayor of the town of Saratoga Springs; however, she has made a national name for herself as speaker at the Republican National Convention and had help in the race from Ann Romney, former U.S. Secretary of State Condoleezza Rice and Sen. John McCain, R-Ariz.