Stoke City 0 Sheffield United 1
Stoke set off at a cracking pace and really should have gone ahead before United retaliated in decisive fashion towards the end of the first half.
Ricardo Fuller was again Stoke's main source of danger, keeping visiting keeper Ian Bennett and his defenders on their toes.
Fuller was close to making the breakthrough in the 20th minute when his shot from John Eustace's pass dipped narrowly over the top.
But the visitors came on strong towards the interval and David Carney should have opened the scoring just before Cahill did just that in the 43rd minute.
Carney's corner from the right sailed over everyone, but Danny Webber drove the ball back across the six-yard line and Cahill buried a downward header.
Stoke again came out bombing at the start of the second half, with Fuller and Mamady Sidibe proving a real handful without seriously testing Bennett, who was given excellent protection by his defence.
Stoke manager Tony Pulis introduced Jon Parkin for the tiring Sidibe in the 66th minute and the big man soon produced a brilliant pass to free Fuller.
But man-of-the-match Cahill made a superb challenge to put the ball out for a corner just as Fuller prepared to pull the trigger.
Stoke also brought on Fuller's Jamaican international team-mate Demar Phillips 11 minutes from time in a desperate attempt to claw back a point.
They continued to pile forward, with a succession of corners and long throws putting the visiting defence under strong pressure.
But Cahill and his team-mates held firm to give manager Bryan Robson some welcome relief before the two-week break.