Goals from Miguel Almiron - his seventh in seven games - Chris Wood, Joe Willock and Bruno Guimaraes ensured all three points headed back to Tyneside, yet again.
Romain Perraud netted a consolation for the hosts.
The game came at a cost though, as Callum Wilson and Kieran Trippier both limped out of the game.
And here’s howe Eddie Howe reacted to the result - and those injuries.
“I’m very pleased with the result, the performance wasn’t our best but I’m not going to pick it to pieces.
“It was a tough game for us, Southampton dropped into bottom three yesterday so we knew they would show a reaction.
“We were not at our best but we scored four wonderful goals.
“It feels a little flat because we didn’t hit the heights which we have in other weeks, but we were clinical when we needed to be.”
“Callum wasn’t that well in the week and felt light-headed and dizzy so that’s why he came off.
“It was a joint decision, he didn’t feel he had the energy needed and it was easy decision to replace him with Chris, who came on and got the job done.
“When you look at today’s performance it was below from where have been but we still won 4-1.”
On Trippier, Howe added: “I’m not sure what happened in terms of him getting treatment. He said he was fine at half-time to carry on. It was my decision to withdraw him at 3-0 just to protect him.”