The result puts Saints up to second in the Barclays U21 Premier League table but their position is under threat from those below them with games in hand.
Liam Smith gave Newcastle an early lead as he pounced on Michael Richardson’s palmed effort.
Reed netted the equaliser on 13 minutes from long-range as he shot from 25 yards and the ball nestled in the bottom corner.
Rowe put Southampton into the lead as he took advantage of a wayward backpass by Macauley Gillesphey and slotted the ball home.
Magpies were level soon after. This time Gael Bigirimana scored similarly to the opener, slotting the ball into an open net.
Rowe scored his second of the game to put Saints ahead before half-time with a neat half-volley – a goal that proved to be the winner.
Saints looked to extend their lead but not even the introduction of highly rated England Under 17 midfielder Josh Sims could secure a more emphatic win.
Watch video highlights below.