United stunned the 2005 European champions a minute into the second half with a Rob Hulse header and though Liverpool levelled with a controversial 70th minute Robbie Fowler penalty, the favourites failed to dominate.
United's outspoken manager Neil Warnock wasted little time in unloading his first salvo of the season at referee Rob Styles.
"I think he made a mistake, there is no way that's a penalty but we'll have to get used to that this season," he told Sky Sports.
"But it's a good start. Everybody's written us off and we've got a point."
The season's first match was delayed as United's biggest crowd for 15 years - 31,700 - squeezed in for the big day.
Liverpool last tasted victory at Bramall Lane in August 1990 when they arrived as champions, never imagining that 16 years on they would still be waiting to add to that record 18th title.
They looked a long way from championship contenders in the first half as United started with all the predictable keenness of Premier League new boys.
Liverpool, who face Maccabi Haifa in the second leg of their Champions League qualifier in Kiev on Tuesday, lost John Arne-Riise to a serious-looking ankle injury after 22 minutes and Jamie Carragher 12 minutes later.
They fell behind at the start of the second half when Hulse was allowed a free header from a David Unsworth free kick.
Liverpool responded well and their pressure paid off when when the referee ruled that Steven Gerrard had been tripped in the box after a one-two with Fowler.
The England midfielder had stayed on his feet as the referee played advantage but as he stumbled the penalty was given and Fowler converted.
Liverpool failed to press on from then though and United were worth their point.
