Noone cashed in on some poor Posh defending to lash in the opener before the break on Saturday and Harley, the recent signing from Swansea, showed his Premier League quality with a fantastic free-kick in the second half.
These are heady days for Gus Poyet’s side, who continue to enjoy life in their new stadium.
The Seagulls remain unbeaten, knocked Sunderland out of the Carling Cup to land a plum tie with Liverpool and, having run away with the League One title last season, are now top of another table.
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.
But three minutes later the hosts made the breakthrough they had been threatening.
Noone collected a miskick from Peterborough goalkeeper Paul Jones and was allowed to move inside, shift the ball to his left foot and crash a low drive into the corner of the net from 20 yards.
Peterborough attempted to hit straight back and Casper Ankergren pulled off a fine save to keep out Grant McCann’s long-range effort and also denied Paul Taylor.
But their cause was not helped when playmaker George Boyd had to leave the field with an injury 10 minutes before the interval.
Brighton could have gone two goals ahead late in the first half but Lewis Dunk’s close-range effort was blocked and Harley put the rebound wide.
Peterborough almost drew level barely 10 seconds after the break when Taylor put Lee Frecklington through to round Ankergren but his shot was cleared off the line by Inigo Calderon.
Full-back Calderon was almost as effective at the other end with a superb run and cross which found Noone, but the winger planted his header over the crossbar.
The second goal came in the 64th minute when Tommy Rowe fouled Barnes 30 yards out and Harley stepped up to curl a stunning free-kick past Jones and into the top corner.
Craig Mackail-Smith had a chance to score against his former club when Noone swung in another cross but the £2.5million striker headed wide.
Peterborough’s best opportunity of the second half fell to Rowe but his shot rolled past the post and with it went the visitors’ chances of getting back into the game.