The launch took place on the same date that NASA's Neil Armstrong and Buzz Aldrin landed on the Moon in 1969, marking a defining moment in the so-called "space race" with the Soviet Union.
A Russian space capsule with three astronauts aboard has docked with the International Space Station after a fast-track trip to the orbiting laboratory.
The Soyuz capsule docked at 22:48 GMT Saturday, just six hours and 20 minutes after blasting off from Russia's launch complex in Baikonur, Kazakhstan.
The launch took place on the 50th anniversary of the day US astronauts landed on the moon.
The capsule is carrying Andrew Morgan of the United States on his first spaceflight, Russian Alexander Skvortsov on his third mission to the space station and Italian Luca Parmitano.
They will join Russian Alexey Ovchinin and Americans Nick Hague and Christina Koch have been aboard since March.
The crew patch for the expedition echoes the one from Apollo 11's 1969 lunar mission.
TRT World's Jon Brain looks back to the Apollo 11's first Moon landing 50 years ago.
'Lucky and privileged'
Speaking at a pre-launch news conference in Baikonur, Parmitano, 42, said the crew were "lucky and privileged" to have their launch coincide with the Apollo 11 date, and indicated that they were wearing badges honouring the anniversary.
Morgan paid tribute to the Apollo 11 landing as a "victory for all of mankind" but ducked a question on whether Russian cosmonauts would ever reach the Moon – the Soviet Union only ever sent unmanned missions there.
NASA was "even more capable" of accomplishing great things when it did so "as part of an international cooperation," Morgan said.
Five decades after the 1969 Moon landing, Russia and the West are still competing in space, even if the emphasis is on cooperation at the ISS.
NASA no longer operates manned flights to the ISS leaving it wholly dependent on Roscosmos' Soyuz program.
But in recent times private companies like SpaceX and Boeing have bid to end the Russian monopoly on manned launches to the ISS, winning multi-billion contracts with NASA.
President Donald Trump, meanwhile, has set an ambitious deadline to return astronauts to the Moon by 2024.
The project – named Artemis – would be the first attempt to send humans to the lunar surface since the last Apollo landing in 1972.
Some experts doubt if the deadline is realistic, given budgetary constraints and delays in developing the next-generation rockets and equipment needed for the journey.
Skvortsov, Morgan and Parmitano all come from military backgrounds and posed together in uniform in the build up to the launch.
Skvortsov joked that "two colonels will be taking orders from a colonel" when Parmitano becomes commander of the space station mid-way through his mission – a reference to the military rank the three share.
The International Space Station has been orbiting Earth at about 28,000 kilometres per hour (17,000 miles per hour) since 1998.