John Armstrong and Robert Dowd each scored two goals and Mathieu Roy registered three assists as Sheffield recorded a 7-1 victory in Guildford.
Dowd put the Steelers ahead in the second minute with a powerplay goal before captain Jonathan Phillips doubled the advantage mid way through the period.
Sheffield went 3-0 up before the break as Armstrong hit the back of the net, though the Flames hit back shortly after the re-start through David Lilliestrom Karlsson.
Any hopes of a comeback from the home side were dashed shortly after however, Colton Fretter scoring a second powerplay goal of the night for the Steelers before Dowd completed his brace.
Sheffield moved further ahead in the third period, Armstrong scoring another powerplay goal for the South Yorkshire side before youngster Liam Kirk rounded off the victory in the 52nd minute.