Johnson was playing his fifth game since coming to Columbus from Los Angeles and his goal 3:54 into the contest gave the Blue Jackets a 2-0 lead.
Columbus, which has the NHL's worst record, has won three in a row for the first time this season.
R.J. Umberger opened the scoring for the Blue Jackets 31 seconds into the game and Derek MacKenzie gave Columbus a 3-1 lead 3:02 into the middle period.
Phoenix has lost four in a row, a skid that has cost the Coyotes first place in the Pacific Division and has jeopardized their bid for a playoff berth.
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