The Avalanche's starting goalie was replaced by Pavel Francouz at 11:15 of the second period when Pat Maroon gave the Lightning a 5-2 lead on their 22nd shot.
Colorado took a 2-0 lead in the best-of-7 series when Kuemper made 16 saves in a 7-0 win in Game 2 on Saturday. It was his first shutout of the Stanley Cup Playoffs.
But Tampa Bay responded Monday with two goals on 12 shots in the first period, and three on 10 shots in the second.
Lightning forwards Anthony Cirelli (13:03) and Ondrej Palat (14:54) finished give-and-goes on the rush to take a 2-1 lead in the first, and Nick Paul scored from the slot at 1:26 of the second to make it 3-1.
Colorado forward Gabriel Landeskog scored his second power-play goal of the game at 4:43 to cut it to 3-2, but Tampa Bay forward Nikita Kucherov set up Steven Stamkos in front for a shot in over Kuemper's glove to make it 4-2 at 7:52.
Kuemper was pulled after Maroon cut in off the left wing and lifted a backhand over his right shoulder.
Kuemper is 8-3 with a 2.76 goals-against average and an .892 save percentage in 13 games this postseason. He returned for the start of the Cup Final after sustaining an upper-body injury in the second period of Game 1 of the Western Conference Final against the Edmonton Oilers on May 31. Francouz started the remaining three games of that series to help complete a four-game sweep.
Francouz, who made nine saves Monday, is 6-0 with a 2.81 GAA, a .906 save percentage and one shutout in seven games (four starts).
Game 4 is in Tampa on Wednesday.
