In his return after missing four games following hand surgery, Kadri cut to the net around Lightning defenseman Mikhail Sergachev on the rush and lifted a shot under Andrei Vasilevskiy's right arm from low in the right face-off circle.
"Sitting here right now it's kind of surreal," Kadri said. "I just was excited to join the team again and be in the dressing room. This is what has I've been working on my whole life pretty much, so it was certainly exciting to get back in the lineup."
Nathan MacKinnon and Andrew Cogliano scored for Colorado, which trailed 1-0 after the first period and 2-1 after the second. Darcy Kuemper made 37 saves.
Anthony Cirelli and Victor Hedman scored, and Vasilevskiy made 35 saves for Tampa Bay, whose eight-game home winning streak ended.
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The Avalanche lead the best-of-7 series 3-1 and can close it out at home in Game 5 on Friday (8 p.m. ET; ABC, ESPN+, CBC, SN, TVAS).
"It's cool, for sure, but we have to focus on how to get the next one," MacKinnon said. "Home ice has been a big thing for us all season, regular season and the playoffs. We'll use it. For sure, the fans are awesome right now. We'll come out fast and hopefully keep it that way."
Tampa Bay came back from trailing 3-2 against the Toronto Maple Leafs in the first round. Now it must win three straight elimination games against Colorado to complete its bid to win the Stanley Cup in three consecutive seasons.
"The feeling [stinks] right now, obviously, but the series wasn't won tonight," Lightning captain Steven Stamkos said. "We know what it feels like to be in their shoes and have a chance obviously to win at home. It's not an easy thing to do. It's a pretty nerve-wracking day.
"For us, our backs are against the wall. We've done it before in these playoffs. We're going to have to do it again."