In the final minute of the third period, Calder broke his left leg when he fell to the ice after being checked.
Only 10,702 fans showed to see the top team in the Eastern Conference outskate the bottom team in the Western Conference for its sixth straight victory. Also winning for the sixth consecutive time was goaltender Nikolai Khabibulin, who stopped 27 shots and stood out when the Hawks launched a late offensive.
"Their big guy in the net made two big saves when the score was 4-3," Hawks coach Brian Sutter said. "We easily could have gotten a point tonight, but we didn't. We knew it would be a wide-open skating hockey game. We made some youngster mistakes in certain situations."
In goal for the Hawks was Adam Munro, 21, who stood out when he made his NHL debut in Monday night's 2-2 tie at Nashville. In that game, Munro had a shutout going until midway through the third period.
This time the multitalented visitors hit him with two short-range goals within a span of 39 seconds early in the first period. Vincent Lecavalier second the first and Fredrik Modin got the second, putting the Hawks down 2-0 with 5 minutes 3 seconds elapsed.
"I figured it couldn't get any worse, so I just tried to relax," said Munro, who finished with 24 saves and earned praise from Sutter for his performance.
"It was a tough start for him," Sutter said. "He kept his poise and made some big saves. Our defense wasn't as sharp with the puck as it has been."
Three times the Hawks reduced Tampa Bay's lead to one goal, thanks to Mark Bell's 19th goal in the first period, Calder's goal in the second and Tuomo Ruutu's 14th on a power-play tip-in midway through the third.
But Cory Sarich's short-handed goal on a blast from the left circle in the second period and Ruslan Fedotenko's goal midway through the third enabled Tampa Bay to stay in control. Brad Richards' empty-netter with 14 seconds to play put the finishing touch on the victory by a surging team that in the last 13 games has won 10 times, tied once and lost twice in overtime.