The Hatters had done enough to win the game by a decent margin but will rue a missed penalty in the 54th minute as they continue their quest for a finish in the top 10 of the Coca-Cola Championship.
Neil Warnock's side have already made second place safe and were only playing to ensure they finished confident ahead of their return to the Premiership next season.
The Blades brought Keith Gillespie and Bruce Dyer into the starting squad while Jonathan Forte and Simon Francis, who have both spent much of the season on loan in Coca-Cola League One, were handed places on the bench.
Luton recalled Rowan Vine and Brkovic to their first XI as they looked to build on last week's impressive 2-1 victory at Plymouth.
The Hatters created the first shot on target in the second minute when Brkovic crossed for Dean Morgan whose mis-hit shot was caught by Paddy Kenny.
Brkovic had a shot blocked by Chris Lucketti soon after as Luton continued to press while Leon Barnett saw his header saved by Kenny.
Dyer was booked in the 26th minute for unsporting behaviour and the former Barnsley man then sent a left-footed shot into the hands of Marlon Beresford as the Blades belatedly fashioned their first chance of the half.
Ade Akinbiyi then saw his close-range effort hacked away by Barnett, who went up the other end of the pitch to force Kenny to parry his header to safety with the final chance of the half.
The Blades were given a lucky escape when Chris Morgan brought down Warren Feeney in the box and the referee pointed straight to the spot. Vine stepped up but blasted the ball over the bar.
The let-off shook United into life and they started to drag themselves into the game as Michael Tonge and Chris Armstrong both created chances while, just after the hour, Akinbiyi volleyed wide.
But it was the home side who took the lead when Brkovic headed home his second goal in as many games from a David Bell cross.
Feeney's long-range effort soon after was punched clear by Kenny and, with nine minutes remaining, the lively Brkovic crossed into the box for Vine whose shot was caught by the Blades goalkeeper.
The home side were unlucky not to go further ahead in the 84th minute when Chris Lucketti fouled Feeney in a dangerous position. Kevin Nicholls fired a free-kick that had Kenny beaten but smashed against the bar and to safety.
But they were left to rue that miss in the 90th minute when United hauled themselves level.
Steve Howard conceded a free-kick and Tonge stepped up to launch the ball into the bottom corner of the net.