Sam Allardyce's side seemed poised to end their three-game losing streak with goals either side of the interval from El-Hadji Diouf and Kevin Davies.
But United's leading scorer Rob Hulse first offered up hope with his fourth goal of the season before an astonishing strike from Colin Kazim-Richards soon after hauled the Blades level.
A frenetic second half was in stark contrast to the first that had little to commend it other than a fine finish from Diouf to end a five-and-a-half-hour drought for the visitors.
The Blades started brightly enough, as they invariably do on home soil, but on this occasion their momentum petered out.
There was an early strike from Hulse in the eighth minute that was comfortably gathered by Jussi Jaaskelainen.
After that the visitors, with Kevin Nolan back skippering the side after serving a three-match ban, rarely found themselves under any undue pressure.
Bolton came within a whisker of opening the scoring in the 14th minute courtesy of Idan Tal, along with Nolan the other change to the side beaten by Wigan last weekend.
Tal narrowly sidefooted a volley wide from just outside the area after Phil Jagielka had headed a Diouf cross into the path of the Israeli.
Eight minutes later Bolton - and Davies in particular - were denied again, sparked by a long ball from Tal from the left wing.
After finding an all-alone Davies four yards outside the area as the Blades defence had gone missing, the striker strode forward and rifled in a shot only for Chris Morgan to produce an outstanding block.
United's best chance of the half followed soon after, with Morgan - starting his first league match for two months in the absence of Claude Davis who sustained a thigh injury in training on Thursday - causing problems in the opposing box.
But in producing a downward header to Derek Geary's long throw, the centre-back wheeled away in anguish after seeing Jaaskelainen turn the ball aside following a despairing dive.
Then virtually from nothing Bolton carved out the opener, created by Henrik Pedersen's raking, curling 60-yard ball down the left that spun away from covering defender Jagielka and into the path of Diouf.
The Senegal forward then held off the challenge of Jagielka before driving a crisp right-foot half-volley from 15 yards across Paddy Kenny and into the far corner of the net.
It would have been 2-0 four minutes from the break but for a fine blocking save from Kenny in denying Tal as the midfielder cracked in an angled left-foot drive.
In need of a spark, Warnock replaced right-winger Keith Gillespie with Kazim-Richards at the break, reverting to three in attack as his side had lacked any potency in the first half.
Instead, it was Bolton's three-man frontline who struck again with their first shot of the second period to pull the rug from under Warnock.
A finely-crafted move started with Diouf's hanging ball from wide on the right being side-footed down by Davies to his left for Anelka.
The Frenchman's incisive lay-off to Tal inside the area allowed the left winger to play the ball back to Davies who drove home his first goal since the opening day of the season through the legs of the advancing Morgan and past a statuesque Kenny.
At that stage Bolton seemed home and dry, but United dug deep to produce their quick-fire double.
Their first riposte arrived in the 70th minute when Christian Nade - a substitute in the aftermath of Davies' strike - combined with Mikele Leigertwood to pick out Kazim-Richards on the right wing.
The youngster delivered a precision cross onto the head of Hulse who powered a header past Jaaskelainen.
Two minutes and 13 seconds later and mayhem ensued inside Bramall Lane courtesy of Kazim-Richards' wonder goal.
A sliding Jaaskelainen could initially do nothing more than push away a long ball pumped forward into the Bolton box, allowing Nade to seize on the rebound and lay off to Kazim-Richards.
From wide on the right and 10 yards outside the area, the 20-year-old struck a first-time right-foot shot that curled its way inside the left-hand post and past the outstretched grasp of an embarrassed Jaaskelainen.
Bolton still had chances for the winner, with Nolan heading into the turf with the goal at his mercy, while Kenny produced another great save to deny a wide-open Abdoulaye Faye.