The story of the game
The Millers were never really in the game at Turf Moor and fell behind to Sam Vokes’ 27th-minute penalty after debutant Lloyd Doyley tripped George Boyd.
Burnley’s winning margin should have been even greater, but Andre Gray headed against the crossbar and then blazed over.
They eventually added a second at the death when Scott Arfield powered home.
But Rotherham should have been level by the point as Joe Newell inexplicably missed a golden opportunity with 10 minutes remaining.
They remain five points adrift of safety after MK Dons were beaten by Bristol City.
The key moment
The Millers had looked barely capable of getting a shot on target until Joe Newell stole into penalty area with 10 minutes remaining, but with the whole goal to aim at he inexplicably put the ball wide.
Grant Ward – Coming off the bench to replace Danny Ward, the on-loan midfielder added energy to the Millers side.
Sam Vokes (1-0 27 minutes) – Vokes made no mistake from the spot, sending Lee Camp the wrong way after Lloyd Doyley’s foul on George Boyd.
Scott Arfield (2-0 86 minutes) – A nice move saw Arfield played in at the far post and he made no mistake, firing past Camp.