A spokesman for Gibbons' campaign said that Gibbons decided to concede defeat just after 11 p.m. as Koster's lead continued to grow.
"We left it all on the table. We did as good as we could possibly do," Gibbons said in his concession speech.
Kinder, of Cape Girardeau, claimed a second term as lieutenant governor over Democratic challenger Sam Page, of Creve Coeur.
Kinder spent two weeks this year lining up support for a gubernatorial run before abruptly switching course. When he instead decided to run for re-election, he went on the offensive even before Page had won the Democratic primary. In their first debate, Kinder called Page a hypocrite who has cast self-serving votes.
Page has accused Kinder of misusing state funds to support pet projects, such as a professional bicycle race, and of allowing state staff to do political work.
In the state treasurer's race, Democrat Clint Zweifel, of Florissant, knocked off Republican Brad Lager, of Savannah. Zweifel, will become the state's youngest state treasurer in more than a century. He replaces Republican Sarah Steelman, who decided to run for governor instead of re-election.
And Democratic Secretary of State Robin Carnahan, of St. Louis, easily won re-election against Republican Mitch Hubbard, of Fulton.
Carnahan was one of the lone bright spots for Missouri Democrats when she won election in the otherwise Republican year of 2004. This year, high-profile Republicans decided against challenging Carnahan, who is the daughter of a former governor and former U.S. senator and the sister of a congressman.
Hubbard, the manager of a McDonald's in Fulton, raised little money. His main issue was criticizing Carnahan about summaries written by her office for ballot measures.
Republican Sam Graves held off Democrat Kay Barnes to win a fifth term in his northwest Missouri district Tuesday, ending what had become perhaps Missouri's nastiest congressional race.
Graves' victory was based on an analysis of current returns and information from voter interviews conducted for The Associated Press by Edison Media Research and Mitofsky International.
With 77% of precincts counted, Graves was leading Barnes 61% to 35%.
The race was one of two House seats that Democrats targeted in the state in hopes of padding their majority in Congress. Republicans worked to keep the GOP's 5-4 advantage among the state's nine House seats.
Democrats also focused on central Missouri's 9th District, where Democrat Judy Baker and Republican Blaine Luetkemeyer were in a heated race to win the open seat created when Republican Kenny Hulshof decided to run for governor.
With 89% of precincts counted, Luetkemeyer was leading Baker 50% to 47.5%.
Barnes was expected to be the strongest challenger Graves faced since he won the seat in 2000. Both candidates raised more than $5 million between them, with Barnes outraising the incumbent. She hoped to benefit from voter discontent with President Bush and a national wave that was projected to help Democrats boost their majority in the House by at least a dozen, and perhaps two dozen seats.