The Sabres have lost four in a row.
Markkanen faced Buffalo for the first time last season with the Edmonton Oilers and recorded a shutout. He was nearly as good in the rematch en route to winning for the fourth time in five starts.
The Sabres did not provide much of a challenge as they were outshot, 34-20, managing only 10 shots in the first two periods combined.
Carter gave the Rangers the lead for good at 2-1 with 10 seconds left in the second. After Buffalo's Chris Taylor failed to clear the puck, Carter recovered on the left of the crease and put a wrister into an open net.