Patrick Bamford put Leeds ahead in controversial circumstances at Elland Road with heavy suggestions of handball after a deflected cross appeared to brush his arm on its way in.
Crysencio Summerville added a second after the break for the dominant Whites and later scored his second from the penalty spot as the hosts made it six Championship wins in succession.
Leeds were aiming to maintain their unbeaten start to 2024 while Rotherham, the Championship’s basement club, were seeking their first win since Boxing Day.
Daniel Farke made six changes from the Leeds side that beat Plymouth in midweek FA Cup action and opposite number Leam Richardson named an unchanged team from that which tasted defeat to Southampton last weekend.
After early Rotherham pressure, Wilfried Gnonto got in behind the Millers but was unable to find Summerville ahead of goalkeeper Viktor Johansson.
Georginio Rutter’s promising cross then found Bamford but his weak effort was claimed by Johansson after five minutes.
Bamford was denied before 10 minutes was played by Hakeem Odoffin’s low tackle after Rutter’s good work as the hosts continued to apply pressure.
Leeds took the lead when Junior Firpo’s left-wing cross deflected off Rotherham skipper Sean Morrison and struck what appeared to be Bamford’s arm to put the Whites ahead.
Rutter’s shot from outside the box flew just over before Summerville wasted a glorious chance after Firpo robbed Odoffin and the winger blasted his 25th-minute effort over, with Rutter being denied by Johansson moments later.
Ethan Ampadu’s fantastic long pass put Bamford through one-on-one but he was unable to control it 10 minutes from half-time.
