The win also saw the Millers close the gap on league leaders Plymouth Argyle - who were beaten by a resurgent Charlton Athletic - to just two points.
Smith has scored 13 goals for Rotherham this season but was suspended for Saturday’s visit of Cambridge.
Ben Wiles, Dan Barlaser and Freddie Ladapo all found the net for the Millers while the visitors’ only goal came courtesy of Sam Smith in the 51st minute.
“Our strength in depth is pretty good and the subs went on and had a positive impact,” reflected Warne.
“You are always going to miss your best players but I thought the two up front did really well. Freddie got a great header and Griggy (Will Grigg) possibly could have scored first half.
“You miss your best players but it doesn’t mean you can’t win without them. It was a good example that we can win if we’re not at our strongest or at our best.”
He added: “I am a big fan of Cambridge and the way they play. They caused problems counter-attacking. Every time we attacked they seemed to break. They put us under pressure.
“You give credit to strikers but I think our back three won us the game. They did some good headers in the six-yard box when the balls were coming in.”
Rotherham United: Vickers; Edmonds-Green, Wood, Harding; Ogbene, Barlaser, Wiles, Ferguson (Miller 64); Sadlier (Lindsay 75); Ladapo, Grigg (Kayode 68). Unused subs: Odoffin, Johansson, Ihiekwe, Bola.
Cambridge United: Mitov; Williams, Masterson, Iredale, Dunk; May, Digby (Wier 87); Smith, Hoolahan (Knibbs 83), Brophy; Ironside. Unused subs: McKenzie-Lyle, Tracey, Okedina, Worman, Lankester.
Referee: A Davies (Hampshire)