Smith's opener and two second-half goals were enough to overcome the disappointing Blades, who failed to return to the play-off places with a third straight defeat and have now won just once in six matches.
Black Cats boss Mick McCarthy brought in Smith and Darren Byfield for Kyle and Marcus Stewart following the midweek win over Wimbledon - and it paid immediate dividends.
Smith gave his side the lead after seven minutes, finishing off a sweeping breakaway. A long clearance was flicked on by Byfield to Smith, who played the ball into the path of Jason McAteer down the right flank.
The Republic of Ireland international held off a challenge from Mark Rankine and his cross to the near post was met perfectly by Smith, who fired a rising shot past Paddy Kenny.
As the game opened up after the break the Blades pushed forward, chasing an equaliser. But it was Sunderland who went closest to scoring again.
Carl Robinson, on-loan from Portsmouth, set off on a jinking run, beating two defenders, but could not beat the on-rushing Kenny with his low shot.
The disappointing Robert Page was withdrawn for Ashley Sestanovich on the hour, but five minutes later Breen wrong-footed marker Phil Jagielka to head home Sean Thornton's corner and double the Black Cats advantage.
Three minutes later, Sunderland had Phil Babb to thank for preserving their two-goal cushion, his outstretched leg blocking Paul Shaw's close-range shot following substitute Wayne Allison's flick-on.
Deep into stoppage time, substitute Kyle latched onto Robinson's long cross-field ball and his low shot back across the goal gave the home side an even healthier margin of victory.
That effort and a long-range Michael Tonge shot aside, the Blades rarely looked like getting back in the game and Warnock's men must reverse their fortunes quickly if they are to stand a chance of finishing in the top six.