Despite putting out a strong side, including first-team regulars Benteke, Andreas Weimann and Fabian Delph, Lambert's players soon found themselves behind.
A disciplined and organised United had comfortably held Villa at arm's length before catching out the Midlands side with their first meaningful attack.
Sheffield United manager Nigel Clough (centre) celebrates after his side's FA Cup win over Aston Villa
Murphy, who had been recalled for Conor Coady, cut inside from the left and scored with a shot which took a deflection off Ciaran Clark on the way past goalkeeper Jed Steer.
Villa lacked urgency and purpose and their response was limited to long-range efforts which failed to test keeper George Long.
The home side belatedly awoke towards the end of the first half and Benteke should have scored when he latched on to an inviting Marc Albrighton cross only to fail to hit the target.
United took the scare as a cue to try to extend their lead and Flynn had a shot palmed wide by Steer just after the break as the visitors continued to frustrate the home side and Villa's agitated fans.
Blades keeper Long had to tip over an Albrighton cross, although it was the visitors who looked more like scoring.
FA Cup fourth round draw
Sunday, 5 January 2014
Cousins Martin and Paul Allen, who both played for West Ham, will make the draw after the Hammers face Nottingham Forest.
Fourth round dates:
Ties to be played over the weekend of 25 and 26 January 2014
Flynn was causing plenty of problems and Steer failed to gather another effort from him before Villa defender Matthew Lowton cleared the danger.
Villa had struggled to break down their stubborn visitors for most of the game, but equalised when a hopeful ball into the box ricocheted about before falling for Helenius to score.
The goal proved a false dawn for Lambert's side as United, who are 51 places below Villa, picked themselves up and scored a deserved winner through the livewire Flynn.
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