The Boro boss has endured a miserable run of results since taking over at the Riverside and he unveiled three new signings from his former club Celtic in an effort to halt the slide.
But the trio of Barry Robson, Willo Flood and Chris Killen could not halt Boro's slide down the table as Cresswell, whose move from Stoke City has now been completed, struck in the 56th minute.
And it was Middlesbrough that carved out the clearer chances in a competitive opening half, Isaiah Osbourne testing Mark Bunn with a low strike that was scooped up on the line by the United keeper.
Robson, fitting comfortably into his midfield birth, picked out centre-back Chris Riggott whose close-range header was snuffed out by Bunn.
United, with just one defeat in their last nine league games, almost found a way through minutes after the restart, full-back Kyle Walker's teasing centre from the right flashing across the face of the goalmouth and beyond the reach of Cresswell and Ched Evans.
It was Cresswell who broke the deadlock as he stretched to beat David Wheater and steer Andy Taylor's cross beyond Danny Coyne from close range.
Boro were seething four minutes later when Jeremie Aliadiere charged into the area only to be sent sprawling as he collided with centre-back Marcel Seip, referee Andy D'Urso waving away their appeals for a penalty.
They could have snatched an equaliser on 63 minutes, left-back Justin Hoyte picking out Flood who scooped his left-foot shot high over the target from 12 yards.
James Harper fired over the top before substitute Henri Camara almost grabbed a second with five minutes left, the ex-Wigan Athletic striker's low strike hitting the foot of the post and rebounding into Coyne's grateful arms.