Kucherov had his first career NHL hat trick, Johnson had four assists, and the Tampa Bay Lightning beat the Coyotes 7-3 on Tuesday night.
''Amazing feeling,'' Kucherov said.
Kucherov got his third goal from slot off a pass from Johnson at 8:23 of the third that made it 5-2.
''They were a lot of fun to watch,'' Tampa Bay coach Jon Cooper said.
Brian Boyle had two goals, and Valtteri Filppula and Matt Carle also scored for the Lightning. Johnson assisted on all three Kucherov goals and extended his point streak to seven games.
Arizona got goals from Shane Doan, Martin Erat and B.J. Crombeen.
''It's frustrating,'' Doan said. I think this is the third game where we've given up way too many goals. As a professional hockey player, you get embarrassed. You have to be embarrassed.''
Arizona has allowed six or more goals three times this season.
Shortly after Radko Gudas had a shot hit the post, Kucherov re-directed the defenseman's next try from the blue line past Mike Smith to put Tampa Bay up 1-0 7:46 into the game.
''He's a dynamic player,'' Johnson said of Kucherov.
After Filppula scored with 7:42 left in the first, Kucherov gave Tampa Bay a 3-0 lead on a backhand rebound at 3:20 of the second.
''I think that first period set the tone for the game,'' said Cooper about the Lightning's 12-3 shot advantage during the opening period.
Arizona has given up the initial goal in seven of eight games this season, and been out-scored 12-5 during the first period.
Doan cut the deficit to 3-1 at 14:07 of the second on his first goal this season and second in 24 career games against Tampa Bay. Antoine Vermette assisted on the Doan's backhander that got past Ben Bishop for his 400th point.
Boyle and Erat traded goals late in the second. Boyle got his second 63 seconds after Kucherov's hat trick during the third.
Crombeen and Carle both added third-period goals.
Smith was pulled after allowing six goals on 33 shots. Defenseman Oliver Ekman-Larsson finished minus-four.
''It's the whole group, not Mike,'' Arizona coach Dave Tippett said. ''There is no excuses here. We didn't play well. Simple as that.''
Bishop made 22 saves.
Notes: Cooper said he would be ''bummed out'' if RW Ryan Callahan didn't return this week from a lower body injury that has sidelined him four games. Callahan declined to address his improved status. ... Arizona C Martin Hanzal played after sitting out three games due a lower body injury and had an assist. ... Tampa Bay C Alex Killorn (four games) and RW J.T. Brown (one game) returned following upper body injuries. ... Lightning D Victor Hedman, who had surgery for a broken finger on his right hand last week and could miss up to six weeks, watched the morning skate from the bench in street clothes. ... F Paul Bissonnette will join Portland, Arizona's AHL team, this week after signing a professional tryout contract.