New signings Barry Robson, Willo Flood and Chris Killen were all included in Boro's starting line-up after joining up with Strachan for a second time.
But Boro have now lost six of their last seven matches and Strachan has only two victories to his name in the 12 games he has taken charge of since being appointed in October.
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Hide AdStriker Cresswell headed his fifth goal for the Blades since his move from Stoke to give Kevin Blackwell's side their third consecutive home win in the league and extend their impressive run to just one defeat in 12 matches in all competitions.