The Soyuz MS-04 spacecraft carrying veteran Russian cosmonaut Fyodor Yurchikhin and NASA rookie Jack Fischer shot into the sky in bright conditions at 1243 IST.
Manned launches to the ISS usually involve three crew members.
But Russian space agency Roscosmos announced last year that only two cosmonauts would travel to the ISS this time as it cuts costs before the installation of a new module to expand the Russian section of the orbital lab at the end of 2017 or in early 2018.
Another Russian-American duo, Yuri Malenchenko and Edward Lu, undertook the last two-man mission to the ISS, in April 2003.
Yurchikhin and Fischer are set to complete a five-month mission at the station.
They are expected to dock at the ISS about six hours after the launch, joining NASA’s Peggy Whitson and Shane Kimbrough and France’s Thomas Pesquet.
In an emotional interview with NASA TV, Fischer, a 43- year-old former US air force pilot, said he would be “thinking about Dad” as he enters orbit.
When dying from cancer, Fischer said, his father encouraged him to pursue his dream of becoming an astronaut.
Yurchikhin, 58, has racked up 537 days in space over the course of four missions to the ISS, more than any US astronaut but some way short of the 879 days logged by record-holding compatriot Gennady Padalka.
The ISS laboratory, a rare example of American and Russian international cooperation, has been orbiting Earth at about 28,000 kilometres per hour since 1998.