Adams was barely a minute from breaking his duck at the eighth attempt when Kevin Lisbie, who snatched a late winner for Millwall against Doncaster last week, repeated the trick to break Blades' hearts.
Daniel Bogdanovic had put the hosts ahead with a contentious penalty 13 minutes from time.
But Lisbie's dramatic leveller means Adams is still feeling the heat at Bramall Lane with his side having taken just three points from a possible 24 since he took over.
Adams, who brought in former Bramall Lane boss Dave Bassett to help out this week, also rang the changes on the pitch by recalling Stephen Jordan, Mark Yeates, Stephen Quinn and Ched Evans.
On-loan Birmingham striker Marcus Bent has not found the net for two years, almost to the day, so typically the first chance of the afternoon fell to him.
Bent was teed up by Yeates but fired his shot too close to David Forde, who made a comfortable block.
Forde was called into action again moments later after Yeates' initial free-kick was blocked, the winger thumping the rebound towards goal only for the Lions keeper to make a fine save.
The best chance of the opening half fell to Millwall winger Danny Schofield, who beat Steve Simonsen to a dangerous cross from striker Robinson but planted his header over the bar.
As half-time approached United were bewildered by a decision from referee Darren Deadman, who booked Quinn for a dive after the midfielder appeared to simply lose his footing in the area.
After the break Forde did well to hold on to a long-range free-kick from Evans before Liam Trotter passed up another chance for Millwall when he headed James Henry's corner over the top.
But the breakthrough Adams and the rest of Bramall Lane were praying for came with 13 minutes to go when Bogdanovic went down under a flimsy challenge from Paul Robinson in the box and stepped up to calmly send Forde the wrong way.
In the last minute Simonsen looked to have secured the points with a fine fingertip save from Lisbie.
But the Blades failed to clear the resulting corner and former Charlton striker Lisbie was on hand to crash the equaliser home.
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