St. Louis would regain the lead late in the first period on a goal by Paul Stastny, and would extend it to 3-1 on a power play goal by Alex Pietrangelo 2:28 into the middle frame.
Zibanejad traded in the assists for his first goal of the season just 30 seconds later. Kreider sent a pass off the boards in the neutral zone that Zibanejad carried into St. Louis' zone and sent a backhand shot on net that found space between Hutton and the post to get the Rangers back to within a goal.
The Rangers had several opportunities to tie the game in the opening minutes of the third period, including a post by Zibanejad and another chance by J.T. Miller that was denied by Hutton.
The final Blues shot on goal coming with 1:16 remaining in the second period. St. Louis managed just seven shots after the first period.
"I don't think we can play much better than we did in the third," Lundqvist said. "We just have to tie it up there. It was close."
Despite the loss, head coach Alain Vigneault was pleased with the way his team played, especially in the final period when it pushed for the equalizer but came up short.
"There was no quit in our team," Vigneault said. "Other than 10 minutes in the first period I thought our whole group played extremely well considering the fact we were down to 5 Ds early."
Defenseman Dan Girardi, who assisted on Kreider's goal, left the game after the second period with a hip flexor. Vigneault said at this time, he'd call Girardi "a little bit more than day to day." He played just 7:56.
The Rangers return home Monday to take on the San Jose Sharks.