F-T: Ipswich Town 0 Rotherham United 1
Victory at Ipswich Town made it four wins and a draw in the last five matches for the resurgent Millers.
They had been six points adrift of a safety spot three weeks ago, but are now in a survival place.
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Hide AdLeon Best scored just before the break and Warnock's men resolutely held out in the face of Town pressure in the second half.
They could even have extended their lead in the 88th minute but Grant Ward shot wide with only the goalkeeper to beat after Greg Halford's supply.
The Millers took the lead in the 44th minute when a lightning break saw Matt Derbyshire produce a perfect low cross from the right and Best was on hand at the near post to steer home his third goal in two games.
Opportunities were few and far between and Warnock's side frustrated Ipswich to such a degree that there were boos from the home crowd as the play-off contenders hit a Rotherham brick wall.
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Hide AdThe Millers had made four changes at Portman Road to the starting 11 against Derby County last week.
Lloyd Doyley came in at centre-half, Halford returned as a holding midfielder, Grant Ward was on the right of midfield and Best, after his two-goal heroics in last Saturday's late comeback from 3-0 down to 3-3, was the lone striker.
Danny Collins, Paul Green and Danny Ward dropped out, although there were places on the bench for Green and Ward, while injury cost Jerome Thomas his place.
Thirteen points out of a possible 15 for Warnock and his men and the great escape is very much on.
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Hide AdIpswich Town (4-4-2): Bialkowski; Chambers, Smith, Berra, Knudsen; Skuse, Douglas (Feeney H-T), Hyam (Bru 74), Pitman (Pringle 70); Sears, Murphy. Subs not used: Crowe, Digby, Foley, Maitland-Niles.
Rotherham United (4-1-4-1: Camp; Kelly, Broadfoot, Doyley, Mattock; Halford; G Ward, Smallwood, Frecklington, Derbyshire (Newell 78); Best (Clarke-Harris 84). Subs not used: Kenny, Wood, D Ward, Green, Burke.
Goal: Best 44 (Rotherham).
Referee: Stephen Martin (Staffordshire).
Attendance: 20,318 (344).