Robert Thomas opened the scoring when he created his own space in the Buffalo zone and put his shot in through traffic 4:47 into the contest.
The Sabres tested Blues netminder Jordan Binnington often early on, making seven saves in the first period, including back-to-back pad stops on Eichel and Lawrence Pilut. He made 17 saves on the night.
Then with 6:31 left in the opening period, Tyler Bozak scored to make it 2-0.
Eichel scored 4:22 into the second period on a great effort. The Sabres captain circled around the net, made his way to the top of the slot and scored in a shooting lane of his own making for his 27th goal of the year.
With 9:43 left in the second David Perron scored on the power play on a shot from the point. Then with 2:36 left, the Blues could've been up 4-1, but Jaden Schwartz's goal was called back after the play was challenged and reviewed, confirming that the Blues were in fact offside during their entry.
However, the Blues were able to go up by three later on when Steen scored 5:36 into the third. He made it 5-1 with an empty-net marker with 4:42 left in regulation.