Bradford chief Stuart McCall hailed his side’s resolute performance as they picked up their first win of the season.
The Bantams had been held to two draws before beating Peterborough.
On-loan Huddersfield strike prospect Jordy Hiwula broke the visitors’ goal drought in the 11th minute and it proved the winner as McCall’s charges stood firm.
“It was an outstanding collective performance from the lads,” said McCall, who picked up his first points since returning to the club.
“We could have made it more comfortable for ourselves, but we have to remember we are only working with probably 13 or 14 senior players at the moment.
“The effort, commitment and desire from the lads, coupled with their play going forward, was fantastic. It would be harsh to single one player out. You could go through the whole side and pick out some outstanding performances. To come to a side who have scored six goals in their first two games and keep a clean sheet is also a positive.”
Hiwula headed Tony McMahon’s cross past Ben Alnwick to give the visitors the lead, which they defended with their lives.
Colin Doyle was made to work for a third consecutive clean sheet as Posh pushed hard. Chris Foster came closest during the first half for the hosts, forcing Doyle into a fine save.
The Bantams backline defended mightily with Doyle pushing Marcus Maddison’s drilled effort past the post after the break.
Peterborough United: Alnwick, White, Baldwin, Bostwick, Binnom-Williams, Maddison, Da Silva Lopes (Chettle 58), Forrester (Anderson 80), Edwards (Coulthirst 74), Nichols, Taylor. Unused substitutes: Smith, Hughes, Tyler, Nabi.
Bradford City: Doyle, McMahon, Vincelot, Knight-Percival, Meredith, Law, Cullen, Devine, Marshall (Anderson 85), Hanson, Hiwula-Mayifuila (Clarke 84). Unused substitutes: Sattelmaier, Webb-Foster, Boateng.
Referee: D Handley (Lancashire).
Man of the match: Romain Vincelot.