The first Falcon 9 Block 5 version blasted off from Cape Canaveral in Florida at 1:14 p.m. Pacific time, lofting a satellite for Bangladesh.
The first stage later successfully landed on an autonomous barge in the Atlantic ocean.
SpaceX says this version of its workhorse launcher can be flown 10 times with only minor maintenance in between flights.
Company founder Elon Musk said the new rocket will eventually make space launches as routine as airline flights.
He said that next year a Falcon 9 first stage will be used for two consecutive launches in the same 24-hour period.