The Brazilian's 73rd-minute goal settled the first leg at St Mary's Stadium in Newcastle's favour though Southampton, which had Duje Caleta-Car sent off late on, had an equaliser disallowed.
Joelinton had a goal contentiously ruled out for handball in the first half and then missed a glorious chance shortly after the restart, but atoned when he converted Alexander Isak's cross.
VAR denied former Newcastle striker Adam Armstrong a leveller less than four minutes later, with Southampton's hopes further dented when Caleta-Car picked up a second booking.
Joe Willock wasted two good opportunities early on, hitting a wild effort over the crossbar after good work from Miguel Almiron before miscuing a volley from Kieran Trippier's cross.
Willock was also involved when Newcastle were denied an opener. Gavin Bazunu parried his shot out to Joelinton, who was contentiously penalised for handball as he fired home the rebound.
Joelinton missed a huge chance seven minutes after the restart, somehow blazing over an open goal from six yards out.
He made no mistake from his next chance, finishing into a gaping net after fantastic play from Isak down the right.
Armstrong thought he had denied his old club with a scruffy finish, only for a VAR review to rule he had handled the ball:
A frustrating outing for the host side was capped when Caleta-Car received his marching orders for fouling Allan Saint-Maximin.
Newcastle spurned chances to further its advantage in stoppage time, but heads into next week's second leg knowing a draw would be enough to book a place in an Carabao Cup final for the first time since 1976.