Kucherov made it 3-0 at 6:11 of the second period with his 22nd goal on a long shot through traffic from the left point. Tampa Bay outshot Arizona 35-18 in the first two periods.
"We weren't sharp at all. We were dull," Coyotes coach Rick Tocchet said. "We did some dumb things out there. I don't know what it is, but we looked really tired and some guys just kind of gave in."
Keller scored his 12th of the season at 11:29 of the second period to make it 3-1, and Johnson scored 31 seconds into the third period for a 4-1 lead. He has a six-game point streak (four goals, seven assists).
Lightning coach Jon Cooper said they entered the game wary of the Coyotes after Arizona swept the season series last season. Tampa Bay missed the Stanley Cup Playoffs by one point and Cooper mentioned a 5-3 loss to the Coyotes at Amalie Arena on March 21.
"We had a 3-2 lead against these guys in our building and ended up losing the game," he said. "We look back at that game and think maybe that was the one that costs us the playoffs, so our locker room was well aware of that."
Lightning goalie Andrei Vasilevskiy made 32 saves for his fifth straight win. He leads the NHL with 21.
Raanta made 44 saves.