Brandon Pirri scored and Roberto Luongo stopped 23 shots for the Panthers.
Florida has lost 10 of 13. The Panthers have only six goals in the last four games.
Phoenix opened a 3-0 lead when Vrbata scored at 5:52 of the third. Vermette fed Vrbata in the right circle and he sent a wrist shot into an open net.
"You score that one and you start feeling good about yourself," Vrbata said. "You get a couple of lucky bounces."
The Panthers closed to 3-1 on Pirri's power-play goal at 8:54 of the third. Pirri's shot from high in the right circle touched several Coyotes players' sticks and went over Smith's glove high in the net.
It was Pirri's first goal with Florida since he was acquired in a trade with the Chicago Blackhawks on March 2.
Smith had been stellar before Pirri's goal.
"Where we are in the standings and the desperation we should be playing with, your goaltender has to take a big part of that," Tippett said. "But it's great to see everybody else chip in."
The back-to-back games appeared to have little effect on Phoenix.
"They played last night. I think we jumped on them early on," Panthers captain Ed Jovanovski said. "We had our chances, we just couldn't solve their goalie."
The Coyotes took a 1-0 lead on a power-play goal in the first. Ribeiro fired a one-timer from above the right circle that got past Luongo on the glove side at 17:43. Keith Yandle got the assist and leads the Coyotes with 45 points. He has seven points in his last seven games.
The Coyotes scored again in the second. Ekman-Larsson shot from just inside the blue line on the left side and it went by a screened Luongo at 9:43.
"They're a very disciplined team, they're patient, they wait for the other team to make mistakes and obviously they're fighting for a playoff spot right now, every game is important to them," Luongo said. "We saw that desperation tonight, guys blocking shot, and finding the net. They did whatever it took to win."
Coyotes forward Martin Erat left in the first period with an upper-body injury.