Murray dominated after saving a break point in the opening game against world number 24 Johnson.
The British number one, 29, will play 13th seed Lucas Pouille of France next.
"I played a very good match. Once I got ahead I managed to keep momentum," said Murray who secured the win in just 74 minutes.
It was Murray's third victory in three meetings with Johnson and was far easier than his 6-0 4-6 7-6 (7-2) quarter-final win at August's Rio Olympics.
The Olympic champion started slowly, but responded to facing a break point in the opening game by playing aggressively - breaking to love in the sixth game to take a 4-2 lead and wrapping up the first set in 40 minutes.
He broke in the third and fifth games of the second set, ending a comfortable victory with 16 winners to Johnson's nine.
"It'll be a hard match," said Murray of his third-round tie with Pouille.
"He goes for his shots, he's a big hitter, he serves well, he's quick around the court. He takes quite a lot of risk out there."
Britain's Kyle Edmund was knocked out in the second round, beaten 6-3 6-4 by Stan Wawrinka.
Edmund, 21, fought back to level the second set after losing five successive games to the world number three.
The Briton had three break-back points as the impressive Wawrinka served for the match, but squandered his chance.
The Swiss, who hit 18 winners to Edmund's six, will next play France's Gilles Simon, who beat China's Wu Di 6-2 6-2.
"I was expecting a tough match because he's improving a lot," Wawrinka said of Edmund.
"I'm happy with the way I controlled the match, serving well. In general, there were a lot of positives for me."
World number two Andy Murray eased into the third round of the Shanghai Masters with an impressive 6-3 6-2 victory over American Steve Johnson.