It was City who started brightly going close through Barry Hayles, before Rotherham took a foothold in the game.
A rejuvinated Mills, who has taken criticism in recent weeks, stole the show with a man of the match display in the middle of the park.
The big man crossed for Broughton to net the opener into first half stoppage time.
The Millers then picked up whwre they left off with a snap Danny Harrison shot before Tonge was put clear by Mills to make it two.
A moment later City responded with Matt Oakley's shot which deflected onto a post and out to safety.
Leicester then rallied again late on but couldn't find a way past Andy Warrington, who capped a great evening with a penalty save from sub Matt Fryatt in injury time.
Rotherham: Warrington, Tonge, Sharps, Fenton, Nicholas, Mills, Cummins (Hudson 88), Danny Harrison, Rhodes, Broughton, Garcia.
Subs Not Used: Annerson, Joseph, Taylor, Yates.
Leicester: Henderson, Hobbs, Kisnorbo, Morrison, Powell, Adams (Berner 61), Oakley, Andy King, Dyer (Chambers 45), Hayles (Fryatt 45), Howard.
Subs Not Used: Martin, Mattock.