"We're almost through it and I was like 'Oh, my God,'" Quenneville said. "I was more worried about killing the major."
Instead of retaliating, the Blues stuck up for Backes by sticking to the game plan.
Shattenkirk said repercussions from the hit are "not for us to focus on."
"We really have to keep just pushing forward," he added. "Whatever happens, just keep a positive mindset, a clear mind."
Tarasenko's second goal of the series was a wrist shot that banged off the right post and in. Kevin Shattenkirk had a goal and two assists for the Blues, who also got a goal from Chris Porter.
Duncan Keith, Seabrook and Michael Rozsival scored in a span of five shots to put the Blackhawks up 3-2 early in the third. But Seabrook's penalty proved costly and the Blackhawks got no help from a power play that went 0 for 4 and is 0 for 9 since Seabrook scored on their first chance in Game 1.
Tarasenko made the most of the Blues' 6-on-4 advantage after pulling goalie Ryan Miller.
Keith's goal late in the second ended a scoring drought of 119 minutes and 27 seconds for Chicago since a three-goal first period in Game 1. Before Chicago's rally, Miller stopped 53 consecutive shots.
A Blues checking forward started the scoring for the second straight game. Porter had one assist in 22 regular-season games.
St. Louis made playing to the whistle pay off, capitalizing on a late flurry when Shattenkirk's slap shot from just inside the blue line beat an out-of-position Crawford with 1.8 seconds to go in the first.
NOTES: Quenneville and Falcons offensive line coach Mike Tice are co-owners of a thoroughbred, Midnight Hawk, that was the prohibitive favorite but lost by a nose in the Illinois Derby on Saturday. ... Shattenkirk had a career-best 10 goals in the regular season. ... Porter, a ninth-round pick of the Blackhawks in 2003, scored his first goal since April 7, 2013, at Detroit. ... Alexander Steen, who got the game-winner in triple-overtime in Game 1, is among five Blues players with two overtime playoff goals. The others: Brett Hull, Pierre Turgeon, Scott Young and Mark Reeds.