The performance came after Vatrano signed a three-year, $18 million contract with the Ducks earlier in the day.
"When you have security, you don't have to think about it anymore," Vatrano said about his new contract. "Put it in the past and just focus on hockey."
Troy Terry had a goal and an assist, Ryan Strome had two assists, and John Gibson earned his 200th NHL victory by making 36 saves for the Ducks (17-18-4), who have won four of five.
“He means everything to us," Vatrano said of Gibson. "He's the longest-tenured guy here now. He’s our backbone. He's a competitor, he wants to win. Guys love him and I couldn't be more happy for him and his family.”
Jake Guentzel scored, and Jonas Johansson made 22 saves for the Lightning (20-15-2), who have lost four straight in regulation for the first time this season.
“We're a really good team, so we just have to come out from the first puck drop, be ready to go from the start, and get back to playing the game that makes us successful," Tampa Bay forward Anthony Cirelli said. "That's playing hard and playing fast. Obviously, not the way we want to start the new year, but we'll go over some video here and look at the things that we can do better and be better at and be ready to go for the next one”
Terry gave the Ducks a 1-0 lead at 5:24 of the first period. He took a drop pass from Strome at the blue line, slowly skated to the top of the right circle, and scored with a wrist shot that went in off the arm of Johansson.
"For our line, we're good friends off the ice," Vatrano said of Strome and Terry. "With our relationships, we can criticize each other jokingly and, also, when we need to say something serious, we listen to each other."
The Ducks extended the lead to 2-0 at 17:03 of the first when Vatrano tipped in Jacob Trouba's shot from above the left circle.