Alex DeBrincat scored twice and Dominik Kubalik added a goal in regulation for the Blackhawks, who lost their first three games to the Lightning this season. Malcolm Subban made 39 saves, plus three more in the shootout.
"We were resilient tonight," Blackhawks coach Jeremy Colliton said. "We gritted it out, whether it's the saves we got or the penalty kills. We blocked a lot of shots and got clears when we needed to."
Anthony Cirelli, Alex Killorn and Ryan McDonough scored for the Lightning, and Curtis McElhinney stopped 24 shots.
Chicago improved to 4-1-1 in its past six games and snapped Tampa Bay's six-game winning streak. On Thursday night, the Lightning won 3-2 in overtime on Alex Killorn's buzzer-beating goal.
"They were probably better last night, and we win," Tampa Bay coach John Cooper said. "Both teams probably know who was a little better tonight, and they end up winning. It comes out even."
McDonough made it 3-2 off a big rebound 3:20 into the third period, jumping on Killorn's drive and beating Subban from 10 feet.
Kubalik tied it 1:40 later by poking home the fluttering shot of defenceman Duncan Keith for his fourth goal in six games.
Overtime started with a flurry of chances for both teams. McElhinney stopped Patrick Kane on a pair breakaways in the first two minutes, and Tampa Bay also had several odd-man chances. Subban held strong despite a hard collision with Steven Stamkos, then denied Victor Hedman, Brayden Point and Stamkos in the shootout.
"We gave up a lot of chances, a lot of breakaways he stopped, and he's the reason we won," DeBrincat said.
Tampa Bay scored twice in the first 11 minutes, only to see Chicago tie it early in the second period.
Cirelli got behind Keith and rebounded Point's shot at 2:51 for his third goal in four games. Killorn made it 2-0 at 10:27 with a power-play goal, tipping Hedman's shot from the high slot.
DeBrincat scored less than three minutes later. The 100th goal of his NHL career was a power-play goal, a wrist shot from the left circle with Blake Coleman off for hooking.
DeBrincat, who had 18 goals in 70 games last season, scored his 14th in 21 games this year 7:08 into the second period, parking low in the left circle before one-timing a pass from Kane to tie it.
"This is a tough challenge," McDonough said of the three-game series with Chicago. "We've got one more crack at them in a couple of days and have to take advantage of it."
Blackhawks defenceman Calvin DeHaan crumpled to the ice after blocking Ondrej Palat's snapshot 2:12 into the final period and eventually limped to the bench. He went to the locker room and did not return.
Tampa Bay played only two overtime games in its first 20 contests but were taken to overtime for the second game in two nights by the Blackhawks, running their season total to four. Columbus and Carolina were the other teams to force the Lightning past 60 minutes, and only Carolina scored a victory.
Blackhawks defenceman Brent Seabrook received a video tribute on the scoreboard Friday night, hours after he announced his retirement because of injuries, saying his right hip wouldn't heal enough to allow him to play following surgery. Seabrook was a key part of the Blackhawks' Stanley Cup winning teams in 2010, 2013 and 2015, as well as Canada's 2010 Olympic champions.
Tampa Bay and Chicago conclude their three-game series on Sunday at United Center.