Johnson put Chicago ahead 3-2 at 17:38 when he finished a 2-on-1 off a backhand pass by Bedard following a Tampa Bay turnover in the neutral zone.
"The first 10 minutes they were possessing the puck," Bedard said. "We showed patience and waited for their mistakes. The guys did great things, and I got the benefits."
Bedard extended the lead 4-2 at 19:52 on another odd-man rush after a Lightning turnover. Johansson made the initial save on Bedard from in close, but Cirelli fell into the goalie, and the puck went in the net.
"He's a good player, don't get me wrong, but we just gave it to him," Tampa Bay defenseman Mikhail Sergachev said of Bedard. "It's totally on us."
Perry made it 5-2 with a power-play goal at 2:12 of the second period with a tip from in front. It was his first game against the Lightning since they traded him to the Blackhawks on June 29.
Stamkos scored at 17:50 of the third period with Johansson pulled for an extra attacker for the 5-3 final.
"Listen, we had the momentum in this game clearly for the first 10-12 minutes, whatever it was,” Lightning coach Jon Cooper said, “and we gave the momentum back with our self-inflicted errors, plain and simple. Turnovers, lack of execution, and we just gave them freebies. It's tough to win if you're going to continue to do that."
NOTES: The two youngest players with a four-point game are Toronto Maple Leafs forward Ted Kennedy (18 years, 27 days; Jan. 8, 1944) and Boston Bruins forward Bep Guidolin (18 years, 58 days; Feb. 5, 1944). … Blackhawks forward Taylor Hall was helped off the ice and left the game at 14:27 of the third after taking a hit along the boards from Lightning forward Michael Eyssimont. Richardson had no update. ... Chicago forward Nick Foligno had three assists. ... Mrazek is 4-12-3 against Tampa Bay. ... Kucherov has a four-game goal streak and 12 points (five goals, seven assists) in that span. ... Stamkos has seven points (two goals, five assists) during a five-game point streak.