The Lightning (40-17-5), who lost 5-3 to the Vegas Golden Knights on Thursday, have lost two straight following an 11-game winning streak. They are second in the Atlantic Division, five points behind the Boston Bruins for first.
"It's extremely disappointing," Lightning coach Jon Cooper said. "We're a much better team than that. We have a system, it's worked well the last three months, and we've got to be better at it."
Andrei Vasilevskiy made 34 saves but allowed a season-high seven goals, or as many as he gave up against the Coyotes in his previous six games against them.
"Maybe we were too accepting of the (Vegas) loss," Tampa Bay forward Pat Maroon said. "Maybe this was just bound to happen. But we can't get too down on ourselves. It's a game where you burn the tape and move on."
Brad Richardson gave the Coyotes a 4-3 lead at 11:04 of the second period after Taylor Hall forced a turnover by Tampa Bay defenseman Braydon Coburn along the end boards and passed to Richardson in the slot. Tampa Bay had scored two straight goals to tie it 3-3.
"They get it to 3-3 and everybody gets down, but the response was big, and everybody got his juice back again," Coyotes coach Rick Tocchet said.
Keller's second goal and third in 21 games made it 5-3 at 11:51 of the third period, and Garland's second goal made it 6-3 at 14:28 on the power play. Derek Stepan scored at 18:46 for the 7-3 final.
"You try to find every weakness (in a goalie)," Keller said. "Every game there's clips of their goalie and the recent goals that he's given up, so I'm definitely going to be watching."
Anthony Cirelli gave Tampa Bay a 1-0 lead at 3:53 of the first period. Garland tied it 1-1 at 17:36, and Keller scored 1:10 later for 2-1 Arizona lead at 18:46.
Carl Soderberg's power-play goal extended the lead to 3-1 at 5:51 of the second. Ondrej Palat cut it to 3-2 at 8:45, and Brayden Point tied it 3-3 at 10:11.
"We kept pressing in the third period and we didn't back up, and that's the way you win in this League," Tocchet said. "When Tampa comes into town, you're on guard because you don't want to be embarrassed, and I felt we stuck with the game plan. When we stick to the game plan, we can be a good team."