Brett Pitman profited from two first-half penalties to put City in command and the visitors' problems worsened when Richard Cresswell received a straight red card for fouling Marvin Elliott just before the break.
Cresswell's lunge into Elliott left the Blades with an uphill battle in the second half and they fell further behind on 62 minutes when Jamie McAllister's right-wing corner floated in at the far post without anyone getting a touch.
Millen said: "That's one defeat in eight games for us now and we are certainly heading in the right direction. We don't like looking too far ahead. We take games in groups of five and set ourselves a points target, which seems to be working well.
"I thought our wingers caused United problems all afternoon and created the space for our strikers to work well together.
"It meant we were able to really stretch our opponents when they went down to 10 men and I was pleased to see us dominate the second half. We've created a bit of breathing space between ourselves and the bottom of the table, but there is a long way to go yet and a great deal more hard work ahead."
Source: PA
Source: PA