The goal ends the longest game in the Blackhawks' 89-year franchise history and broke the streak of 110 consecutive scoreless minutes. Brent Seabrook assisted Kruger on the game-winner, while Shaw and Marian Hossa added power play goals in the victory.
The game also marks the longest game in Honda Center history.
Andersen made a career-high 53 saves for Anaheim in the loss. Meanwhile, Corey Crawford responded with 60 saves to help Chicago hand the Ducks their second loss of the postseason.
Tuesday's game 2 was the 17th longest game in NHL history, and longest game since the San Jose Sharks and Dallas Stars played four overtimes on May 4th, 2008.
Shaw's goal was not allowed at 8:47 of the second overtime period on the power play, as he headbutted Patrick Kane's shot in. After review, officials ruled it illegal, which many current players and fans had no idea was in the rule book.
Corey Perry and Andrew Cogliano scored Anaheim's goals, as they fell to 9-2 in this season's playoffs. They were shut out over the final 78:42 of game time, falling at home for the first time in seven games. The Ducks hadn't played a game with multiple-overtimes since May 3rd, 2009, while the Blackhawks won two multiple-overtime games in the first round against the Nashville Predators.
Tuesday's game was the second-longest in Ducks' history, trailing a five-overtime game against the Stars in 2003.
Game 3 of the Conference Finals will head to Chicago on Thursday night.