In a king and pawn endgame…
King on the 6th rank, pawn on the 5th rank (not on the a or h file) wins regardless of whose turn it is to move. The king on the 6th rank uses the opposition to push the opposing king aside.

4k3/8/4K3/4P3/8/8/8/8 w - - 0 1
The white pawn will promote.
The black king can stop the white pawn if the pawn is on the a or h file.