Byrne netted twice in the second half after Andreas Pereira gave the young Reds the lead on 19 minutes following good work by Byrne.
Southampton went into the game three points clear of Paul McGuinness' side in the Barclays Premier League Under-18s Group 2 table and beat United 4-2 only last month. But at a blustery Trafford Training Centre, they were no match for a strong United side.
Byrne was the star and it was his shot, following a wonderful piece of skill, that proved too hot for the Southampton goalkeeper to handle on 19 minutes. Pereira tapped in the rebound to send the Reds 1-0 up.
The visitors began the second half menacingly but United's counter-attacking play was also causing problems and on 64 minutes Byrne netted with a terrific header at the near post from Jack Barmby's cross.
The Dubliner capped a fine performance and completed the scoring with 12 minutes to play when he cut inside off the left touchline and curled a stunning effort into the top corner.
Victory takes United above Southampton and into second spot, by way of a superior goal difference. The young Reds' next test comes in the shape of Everton on Wednesday 17 April (11:00 BST).
United: Gollini; Love, Evans (Ioannou 46), McNair, Grimshaw; Pearson, Weir (Daehli 25), Rudge, Byrne; Pereira, Barmby (Wilson 65)