There were opportunities and openings aplenty but Sheffield United were forced to wait until the 88th minute before grabbing the goal which settled this thoroughly entertaining game.
Predictably, it was scored by their captain Billy Sharp who, after turning home James Hanson's header, has now claimed 20 since the start of the campaign.
Peterborough, having more than contributed to what proved a compelling spectacle inside London Road, will count themselves unfortunate not to have finished with a share of the spoils. But football is all about results, not fairness and, under Chris Wilder's management, United have become a very ruthless bunch.
Moving five points clear of second placed Scunthorpe at the top of League One, the visitors were pushed all the way by Grant McCann's charges before landing a devastating and decisive blow.
Sharp will dominate the headlines but Jake Wright's performance at the heart of United's back three was also worthy of a mention as he made a series of crucial blocks and interceptions to prevent Peterborough bursting through.
Jay O'Shea also impressed on his first appearance for United, who were roared on by a travelling army of over 4,000.
There is still a long way to go in the battle for promotion and Tuesday's trip to Bristol Rovers is expected to be another stern test. But the manner of their win only serves to underline the fact that United have both the persistence and the quality to go all the way.
With Ethan Ebanks-Landell and Paul Coutts both nursing injuries, United made two changes to their starting eleven. Samir Carruthers, who has made two substitute appearances since leaving MK Dons last month, and Chris Basham profited from their team mates' misfortune. Both acquitted themselves well enough. But, after surviving a good spell of Peterborough pressure, it was Hanson and John Fleck who caused Peterborough the most problems. Although, during the dying embers of the first-half and early stages of the second, Daniel Lafferty also enjoyed two good chances to break the deadlock.
Hanson scored twice at this stadium for Bradford City last season and could easily have claimed another brace before creating the opportunity for Sharp to score.
In the 40th minute, following a driving run by Billy Sharp, he was foiled by Luke McGee before dragging wide on the rebound. In the 50th minute, the on-loan goalkeeper came to Peterborough's rescue again when Hanson met a cross on the edge of the six yard box.
Like United, Peterborough were bright, positive and purposeful during the opening exchanges although, unlike the visitors, McCann's players initially proved unable to pick the right pass. After Sharp had been adjudged offside, Gwion Edwards ballooned a long-range attempt way over Simon Moore's crossbar before Jerome Binnom-Williams twice found touch rather than a team mate.
As the half progressed, though, so Peterborough's precision improved. Indeed, they will have been disappointed not to have embellished a good spell of pressure with a goal midway through the first-half when Craig Mackail-Smith burst forward. The fact they failed to make the most of the situation was down, full-square, to Wright. Taking a moment to assess the situation as the on-loan forward and Marcus Maddison attacked, Wright opted to stand his ground rather than chase the ball. It meant, rather than being cut out of the action, he intercepted what would almost certainly have been a goal-creating pass.
Hanson and Lafferty both had shots blocked in quick succession before Maddison went close with a 30 yard set-piece. That passage of play summed up the action so far, with United threatening on occasion while Peterborough looked the more likely to score. As the interval approached, Wilder's players got to grips with the game. Hanson was thwarted by McGee as he attempted to caress the ball into the back of the net. McGee denied the United centre-forward again just before the hour. The introduction of O'Shea for his United debut brought a different dynamic to their play. Unfortunately, the increasingly erratic decision making of referee Andy Haines made it tough for either team to build any momentum. But, just as the contest seemed destined to finish all square, Hanson headed a deep cross into Sharp's path and the 31-year-old did the rest.
Peterborough United: McGee, Smith, Tafazolli, Edwards (Forester 62), Maddison, Ball, Mackail-Smith, Inman (Samuelsen 88), Nichols (Morias 62), Binnom-Williams, Grant. Not used: Tyler, Hughes, Baldwin, Forrester, Angol, Samuelsen, Morias.
Sheffield United: Moore, Fleck, O'Connell, Basham, Sharp, Wright, Hanson, Freeman, Duffy (O'Shea 62) , Lafferty (Lavery 78), Carruthers (Riley 88). Not used: Long, McNulty, Done, Riley, Wilson.
Referee: Andy Haines (Tyne and Wear).
Attendance: Not given.