Big Sam's Bolton side looked to have sealed the win to maintain their grip on the Premiership third place until Neil Warnock's warriors battled their way back.
A clever goal from El Hadji Diouf in the first half put Bolton in control and when Bramall Lane reject Kevin Davies added the second after 59 minutes home fans feared the worst.
But Warnock, an unashamed admirer of Allardyce and all that Bolton have achieved, yelled for more from his side and they responded impressively.
First Rob Hulse claimed his fourth goal of the season on 70 minutes, triggering Big Sam's arrival in the dugout for the first time.
He had barely warmed his seat when the equaliser came from Kazim-Richards with a superbly place shot to beat Jussi Jaaskelainen.
Warnock, who had warned this clash would be one of the season's toughest celebrated along with the fans and players to underline how important this win was.
It started as a dreary scrappy affair until the opener from Diouf.
He pounced 11 minutes before half-time when the Senegalese showed his class. Henrik Pedersen launched a long ball down the left and Diouf chased it before cutting inside and shrugging off a limp challenge from Phil Jagielka.
He flicked the ball cleverly from his left foot to his right and hoisted it over the advancing Paddy Kenny.
Then after 59 minutes, Davies, rejected by United after being a junior at the club, latched on to a clever lay-off by Idan Tal and drilled in a low shot from 20 yards.
Hulse, though, who had worked tirelessly, earned his reward when he powered in his fourth goal of the season, heading in a sweet cross from Mikele Leigertwood.
And three minutes later 20-year-old £150,000 September signing from Brighton Kazim-Richards had the last word.
Jaaskelainen blocked a dangerous ball into the area and Christian Nade pounced on the loose ball and slipped it to Kazim-Richards, who curled a sweet shot out of the keeper's reach.
Late saves from Kenny kept Bolton at bay as they looked for the winner, but both sides had to settle for a point after a thrilling end-to-end encounter.