In a game of few chances, the visitors had the bulk of the possession, but Richard Wright had little to do, although he made one world-class save to deny Matt Kilgallon.
The game began slowly and it was 26 minutes before a meaningful attempt on goal with Paddy Kenny tipping away a fierce low drive from David Norris.
A minute later, Pablo Counago sent a 20-yard snap-shot against the post, before Brian Howard put a free header over from Quinn's cross at the other end.
Alex Bruce put a free header wide from a Darren Ambrose corner before Town went ahead when Kilgallon handled Jon Stead's cross and Miller sent Kenny the wrong way with his penalty.
Sheffield United came out strongly in the second half with Beattie twice volleying over, while Kenny produced a fine diving save to deny Moritz Volz.
Town had a great chance for a second goal on 58 minutes when Kenny flapped at an Ambrose corner and Bruce's goal-bound shot was headed clear by Gary Naysmith.
Wright made a sensational save to deny Kilgallon from four yards as he met a Howard corner and it looked as if Town would hang on.
However with a minute left, Quinn pushed away a Beattie 20-yard shot to concede an obvious penalty and Beattie made him pay by sending Wright the wrong way.