Loan striker Hurst netted a memorable brace as the Shakers looked to take full advantage of Jason Puncheon's red mist.
But a controversial penalty ten minutes from time allowed the visitors to snatch a share of the points with skipper Ian Hendon putting away the spot-kick.
Earlier, Hurst, who had spent less than 24 hours with his new club after agreeing a one-month deal at Gigg Lane, gave the home side a 15th minute lead. His cool strike was too good for Barnet keeper Lee Harrison.
Quick feet from striker Andy Bishop released Hurst, before a sweet left-foot strike flew past Harrison to give the Shakers the lead.
And it should have been 2-0 a minute later when Marc Pugh, back in the Bury side after injury, danced past two defenders, only to drag his right-foot shot wide from inside the box.
Bury were made to pay when, five minutes later, Barnet drew level. A pinpoint cross from the left from Puncheon found centre-forward Tresor Kandol lurking at the back post and his looping header proved too much for Schmeichel.
Puncheon was sent off 11 minutes into the second half for kicking out at defender Paul Scott.
Hurst grabbed his second in the 74th minute, latching on to a cross from Scott, and should have had a hat-trick two minutes later, but fired into the side-netting.
However, the turning point came when Manchester City loan keeper Kasper Schmeichel was adjudged to have fouled Ismail Yakubu in the box.
It looked a harsh decision from Tyne & Wear referee David Foster, but Hendon didn't miss his chance from the spot and earned a share of the spoils for the Bees.