It leaves them with four points from their opening two games, after a turgid goalless draw with Sheffield United at the Riverside Stadium last Friday, and left Southgate purring.
"It feels sweet to win away but the manner of the win was pleasing. ee pressurised Swansea well and didn't let them get into their stride," he said.
"We are a young and vibrant team in a league which is wide open. It's only one win but we have to be more ruthless and take our chances."
Johnson, an England U21 international, scored the first goal for Boro and earned himself special praise from Southgate.
"He was really good and we wanted to get the ball to him as much as possible," he said.
"He was a constant threat to Swansea. He, like many of our players, has played at this level before and he wants to get back to the top.