With the Lightning leading 3-2, Johnson doubled the advantage with 5:22 remaining and then completed his first career hat trick less than 2 minutes later. The rookie center has 16 goals this season.
Mark Barberio and Valtteri Filppula also scored for the Lightning. Martin St. Louis extended his point streak to 10 games with an assist on Johnson's second goal.
John Mitchell and Tyson Barrie scored in the second period for Colorado.
Sami Aittokallio made his first start this season and second of his career filling in for injured Colorado backup Jean-Sebastien Giguere (back). Playing three times in four days, Avalanche coach Patrick Roy had planned to give Semyon Varlamov, who made 34 saves in Friday's 3-2 win at Florida, the night off.
Varlamov replaced Aittokallio, who gave up three goals on 18 shots, to start the third period.
Aittokallio, recalled from Lake Erie of the AHL Friday, made his first career appearance in a start last April 11 at Los Angeles, a game in which he left in the third period due to leg cramps.
Johnson opened the scoring at 7:15 of the first period, Barberio made it 2-0 about 1 minutes later when his shot from the top of the right circle deflected off a Colorado defender and past Aittokallio. Filppula completed Tampa Bay's three-goal period with just under 2 minutes to go.
Mitchell got the Avalanche on the scoreboard when his redirection eluded Ben Bishop with 1:27 left in the second and Barrie scored 30 seconds later to pull Colorado within one.
NOTES: This was the first game in Tampa between the teams since Dec. 4, 2010. ... Roy never won a road game as a goalie against Tampa Bay, going 0-7-1, during his Hall of Fame career. Roy, the first-year Colorado coach, is second on the NHL goalie victories list with 551. ... Lightning star Steven Stamkos did light contact drills for the first time during the morning skate since breaking his right shin last November. ... Colorado LW Alex Tanguay, who returned Friday after missing 36 games with knee and hip injuries, had a scheduled night off.