Doncaster Rovers had to settle for a point when Sheffield United scored in the fifth minute of injury time to equalise.
Despite being reduced to ten men early in the second half, Rovers looked to be heading for three points with two goals from Billy Sharp.
Bogdanovic got United back into the game with four minutes of normal time remaining and Kozluk equalised deep into stoppage time for a share of the spoils.
Sean O`Driscoll made two changes from the side that beat Scunthorpe United on New Years Day.
Injured duo Shelton Martis and Brian Stock were replaced by Dennis Souza and Dean Shiels.
Rovers almost took the lead in the opening minutes when Kyle Bartley almost put through his own net; his blushes were spared by a great save from Simonsen.
United had a couple of early chances but both Kozluk and Evans shot wide.
In a lively start, John Oster was next to have a chance when he fired a free kick over the bar.
The game became very stop start with a number of free kicks stopping any momentum in the game.
The referee was forced into issuing two yellow cards inside the first twenty minutes with Kozluk booked for United and Souza for Rovers.
With over 35 minutes gone, the home side were still waiting for their first shot on target and Evans headed their next chance over the bar.
Billy Sharp thought he`d given Rovers the lead when he fired into the net but an offside flag ruled his effort out.
The sides went in at half time with either side able to break the deadlock in a tight battle.
Sheffield United started the second half strongly and Evans finally tested Sullivan in the Rovers goal.
Bartley and Evans again forced Sullivan into saves as the home side searched for the opening goal.
Rovers suffered their second red card in two games when Dennis Souza received his marching orders after collecting two yellow cards on 58 minutes.
Sean O`Driscoll quickly reshuffled his side with James Chambers coming on for Dean Shiels.
Doncaster took the lead on 66 minutes when Billy Sharp scored on his return to his former club when James Coppinger crossed and Sharp showed composure to beat Simonsen.
James Coppinger was then brought down by Kozluk inside the area to earn Rovers a penalty and that man Sharp scored again from the spot to make it two nil.
The home side had appeals for a penalty turned down when there appeared to be a handball inside the area.
United tried to find a response and Montgomery forced Sullivan into a good save.
Hayter almost made it three nil when his effort from the edge of the area hit the side netting.
They did get a goal back with just four minutes remaining when Daniel Bogdanovic fired home.
United were throwing the kitchen sink at Rovers and the defence were standing strong. Sean O`Driscoll made his final substitution of the afternoon bringing defender Webster on for Coppinger.
The fourth official put his board up to show seven minutes of added time to the despair of Rovers who were hanging on with their ten men.
Montgomery again went close for United when he just fired wide of the post.
Billy Sharp was substituted deep into injury time and he was greeted by a chorus of boo`s from the home fans. They were obviously gutted to see what he was capable of when playing with a side that play football and not hoofball.
United continued to probe for an equaliser and Sullivan again was called into action to deny Britton.
The home side eventually got the equaliser in the fifth minute of injury time when Kozluk beat Sullivan from close range.
It was to prove the final action of the afternoon as a storming second half saw the teams share the points.
Teams
Sheffield United
Simonsen, Montgomery, Ertl, Evans, Yeates, Williamson (Harriott 84), Cresswell (Bogdanovic 78), Ward (Britton 72), Kozluk, Bartley, Parrino
Subs not used
Calve, Long, James, Slew,
Doncaster Rovers
Sullivan, O`Connor, Lockwood, Mills, Souza, Coppinger (Webster 89), Shiels (Chambers 61), Oster, Wilson, Hayter, Sharp (Healy 90)
Subs not used
G. Woods, Brooker, Gillett, Healy, Fairhurst
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