After seeing their 3-0 lead cut to one goal in the third, Andrew Sharp added two goals in the final period to seal the game and tie the series 3-3.
Shaw had scored just twice during the play-offs but caught a timely surge to set up a Saturday showdown in Anaheim.
Chicago centre and captain Jonathan Toews said: “I think when we realise that our season is on the line, we kind of think back to everything that got us to this point and realise the opportunity we have and the group we have, throw everything in the mix and that’s the motivation we have.”
Patrick Maroon and Clayton Stoner scored for the Ducks as they tried to rally back, but fell short and Anaheim coach Bruce Boudreau said: “We lost our composure, I thought, for the first time in the play-offs. They scored the first goal, and then started scoring all over.”
Chicago goalie Corey Crawford stopped 30 of Anaheim’s 32 shots, while Anaheim goalie Frederik Andersen made just 18 saves. Chicago got their second-period scores from Brandon Saad, Marian Hossa and Patrick Kane.
The goal was particularly significant because Hossa has struggled to score in the play-offs. After being one of the team’s top scorers (22 goals) during the regular season, Hossa’s goal on Wednesday was only his third in 16 play-off games this post-season.
The Ducks are looking for their first trip to the Stanley Cup Finals since 2007, while the Blackhawks won titles in 2013 and 2010.