We didn't eliminate mosquitoes, but we aggressively reduced their populations. Malaria eradication was almost entirely due to widespread use of DDT, as well as draining swamps where mosquitoes breed.

The National Malaria Eradication Program was a cooperative undertaking by state and local health agencies of 13 southeastern states.... The program commenced operations on July 1, 1947. It consisted primarily of DDT application to the interior surfaces of rural homes or entire premises in counties where malaria was reported to have been prevalent in recent years. By the end of 1949, more than 4,650,000 house spray applications had been made. It also included drainage, removal of mosquito breeding sites, and spraying (occasionally from aircrafts) of insecticides. Total elimination of transmission was slowly achieved. In 1949, the country was declared free of malaria as a significant public health problem.

http://www.cdc.gov/malaria/about/history/elimination_us.html