Craig Noone and Ryan Harley scored stunning goals either side of half-time as unbeaten Brighton moved top of the Championship.
Noone cashed in on poor defending to fire in the opener from 20 yards.
Posh almost drew level seconds after the restart when Lee Frecklington rounded keeper Casper Ankergren but Inigo Calderon cleared off the line.
Harley wrapped up the points when he curled home a stunning 30-yard free-kick in the 65th minute.
Gus Poyet's side remain unbeaten at their new Amex Stadium following their promotion season from League One.
They should have taken the lead in the seventh minute when Noone escaped down the left and pulled the ball back for Ashley Barnes on the penalty spot but the striker missed the target.
Three minutes later, Brighton got the breakthrough they had been threatening when Noone collected a miskick from Peterborough goalkeeper Paul Jones before cutting inside and crashing home a low drive from 20 yards.
Peterborough almost hit straight back but Ankergren pulled off a fine saves to deny Grant McCann and Paul Taylor.
And they suffered a further blow when playmaker George Boyd was forced off through injury 10 minutes before the break.
Brighton almost doubled their lead just before half-time but Lewis Dunk's close-range effort was blocked and Harley put the rebound wide.
Noone then went close to a second with a header before Harley finally struck.
Peterborough's Tommy Rowe fouled Barnes 30 yards out and Harley stepped up to curl a brilliant free-kick past Jones and into the top corner.
Late on, Seagulls' record signing Craig Mackail-Smith had a chance to score against his former club late but the £2.5m striker headed wide.
Brighton manager Gus Poyet:
"We are top of the table and deserve to be, although it's very, very early.
"We were professional today and knew we had to be organised at the back.
"As soon as we scored, the game opened up a little bit, and although Peterborough tried their best to come back at us they had mainly to rely on shots from long distance."
Peterborough assistant manager Kevin Russell:
"For long periods there wasn't much between the teams, but we only created two chances. Our final ball was very disappointing.
"We are extremely disappointed with the first goal, in particular, as it was a poor goal all round.
"If goalkeepers make mistakes at this level, they are punished. That is football.
"Our two centre-halves, Gabriel Zakuani and Ryan Bennett, were outstanding. But we desperately lacked a cutting edge, and we never looked like getting past the Brighton defence."