The game remained tied until 4:22 of the second, when Anthony Cirelli hacked home a loose puck at the post to put the visitors on top 2-1.
Tampa began to pull away at 12:07 of the second, when Tyler Johnson finished off a passing play to give the Lightning a 3-1 advantage.
Brayden Point's goal at 14:01 of the middle frame made it a 4-1 game. Victor Hedman made it 5-1 in the third.
However, David Kampf sniped a nice goal at 15:17 of the final frame from the slot. The Blackhawks also made it more interesting with 3:48 left on the clock when Nick Schmaltz scored to make it 5-3. The play was initially ruled a no-goal, but was reviewed and reversed after the officials determined it did indeed cross the line.
An empty-netter made it 6-3 for the Lightning with just over two minutes remaining, putting the stamp on the visitors' victory.
FORTIN'S FIRST:As a young player, you'd like your first NHL goal to be one to remember - a highlight-reel worthy moment. How about a breakaway equalizer? Fortin, who had been close in his first handful of games to lighting the lamp, put all his frustrations behind him when he received a pass behind everyone and beat Louis Domingue one-on-one at 11:40 of the first period. He now has points in two straight.