Two Luciano Becchio goals clinched a deserved 2-1 victory for the Whites in a game that was comfortable for them until the closing stages when winless Peterborough pulled a goal back and made a fight of it.
After losing by the same score in midweek it was a marked improvement from Leeds, both up front and in defence.
Warnock said: "We deserved it but it was a bit hair-raising towards the end when we couldn't finish them off.
"You get greedy but we should have had a third goal on the break. That would have made it easier and you know Peterborough will fight for their lives. You get a comeback if you're not careful.
"The back five were fantastic and the players are getting better with each game and our forwards were terrific.
“The front four players were poor in the defeat at Blackpool and I let them know as much but they were much better today.
“We looked dangerous, Luciano got his goals and we did a very professional job"
Peterborough United 1
Leeds United 2
(Becchio 7, 50)
Saturday, August 25, 2012
Peterborough: Olejnik, Alcock (Little 62), Brisley, Zakuani, Nthie, Bostwick, McCann, Frecklington (Swanson 62), Tomlin, Boyd, Sinclair (Taylor 64).
Leeds: Kenny, Peltier, Lees, Pearce, Drury, Diouf (Byram 75), Austin, Norris, Varney, McCormack (Poleon 78), Becchio (Gray 87).
Referee: Scott Mathieson.