UNITED 3 (Beckford 62, 71, Howson 90), PETERBOROUGH 1 (Mackail-Smith 80)
United: Ankergren, Hughes, Marques, Naylor, Dickinson, Robinson (Snodgrass 88), Douglas, Delph, Johnson, Becchio (Beckford 59), Trundle (Howson 82). Subs: Lucas, Michalik.
Peterborough: Lewis, Morgan, Martin, Zakuani, Lee, Whepldale (Batt 90), Keates, Coutts, Boyd, Mackail-Smith, McLean. Subs: McKeown, Torres, Crofts, Blanchett.
Referee: A Taylor
Booked: Delph (United)
Att: 22,766
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United manager Simon Grayson recalled Andy Robinson to the starting line-up in place of the injured Frazer Richardson, while loan signing Richard Naylor marked his home debut by being made captain for the clash against Peterborough.
Visiting Posh were looking to close the gap on second placed MK Dons while Leeds were aiming to reduce the five-point gap to the Play-Off positions.
It was a tentative opening, and the first shot at goal came on seven minutes when Lee Trundle turned inside the box before lifting his angled shot over the top.
Trundle also won a free-kick on the edge of the box, following a foul by Dean Keates, with Bradley Johnson's low-free kick taking a deflection for a corner.
Rui Marques also had an effort blocked from the resultant corner before the visitors finally cleared their lines.
Peterborough threatened after 18 minutes when George Boyd headed wide and Craig Mackail-Smith lifted a shot over the top.
The duo had scored the Peterborough goals at London Road in October, and Boyd tested Casper Ankergren for the first time on 22 minutes with a shot from distance.
But it was United who almost snatched the lead when Joe Lewis made a terrific save to deny Robinson who got on the end of a Jonathan Douglas shot.
And on 27 minutes Lewis denied Robinson again when he got down well to palm a low shot onto the post. At the other end, Ankergren made a good save to deny Boyd.
Five minutes before half-time, Trundle went close for Leeds with a glancing header.
But it was the visitors, the liveliest side to visit Elland Road so far this season, who started the second period brightly and on 52 minutes Boyd lifted a shot over the top. Moments later, Aaron McLean fired over from a tight angle.
United hit back on 57 minutes when Trundle showed good skill to win a corner and the game continued at a good pace with both sides threatening.
Moments later, Grayson made his first change with Jermaine Beckford replacing Becchio in the front-line.
And the striker made an immediate impact when Posh goalkeeper Lewis parried a Bradley Johnson free-kick, and Beckford pounced to give United the advantage with a shot from close range.
That advantage was almost doubled when Lewis spread himself well to deny Trundle, following great work from Fabian Delph.
And it was 2-0 in the 71st minute, courtesy of Beckford's second goal. Trundle was the provider with a tremendous ball forward and Beckford showed great composure before tucking the ball beyond Lewis.
But there was a twist in the tail with 10 minutes remaining when the visitors pulled a goal back. Boyd headed a Chris Whelpdale cross against the bar and, despite the best of efforts of Naylor, Craig Mackail-Smith was on hand to apply the finishing touch.
Four minutes of stoppage time should have been the cue for the visitors to summon up one final effort, but the game was sealed in the first minute of added time by substitute Jonny Howson.
Howson swept the ball home to guarantee Grayson's first home win as United manager and to make it three wins from four games.
