Last year's U.S. Open finalist beat the American 6-7 (7-9) 6-1 6-2 6-3 after a tough opening set. Nishikori defeated Johnson in the second round in Brisbane a fortnight ago.
Johnson got off to a flying start and the two men exchanged breaks in the opener. The set went to a tie break, which Johnson won 9-7. Nishikori was far more dominant in the next two sets, taking only 33 minutes to win the third set.
The American tried to stage a return in the fourth set, but when Nishikori took a 4-3 lead it was all over.
He said: "It was a nice battle and I was playing solid in the last couple of sets, so it was a very good win today.
"I was a little bit nervous early but I started to get the rhythm and started to play solid, so I am very happy to go through.
"I think from now on it will be a tougher opponent coming up, but I’ve won three good matches so it was exciting to play here today."
Nishikori will be looking to book his place in the quarter-finals with a victory over either David Ferrer or Gilles Simon on Monday.