Danny Ings' double helped Southampton to a famous 4-0 win over rivals Portsmouth at Fratton Park in their first meeting since 2012.
Pompey dominated the opening exchanges as Brett Pitman struck the post before Ryan Williams' shot was cleared off the line, but Danny Ings (22) struck from outside the box against the run of play, before doubling his side's lead on the stroke of half-time.
The hosts failed to reduce the deficit before a clinical Saints put the game to bed with Cedric Soares' close-range effort (77) before Nathan Redmond added a fourth five minutes from time.
The victory is Southampton's first at Fratton Park since 1984 and their biggest away win over their south-coast neighbours.
How the Saints silenced Fratton Park
The hosts started brightly and, cheered on by a fiercely partisan crowd, should have taken the lead in the opening 20 minutes. Pitman wrong-footed Saints 'keeper Alex McCarthy only to see his shot strike the post, before Jan Bednarek cleared Williams' close-range shot off the line.
But Saints showed their Premier league quality when James Ward-Prowse fed Ings on the edge of the box, his exquisite first touch creating space for a shot that flew through Portsmouth's defence and into the net.
Pompey rallied and Oliver Hawkins almost equalised from 10 yards, but Ings again proved the difference when he latched onto Michael Obafemi's wonderful pass to dink over the on-rushing Craig MacGillivray and double his side's lead just before half-time.
Southampton managed to take the sting out of a Portsmouth fightback in the second half, limiting their opponents to long-range shots, despite the best efforts of the marvellous Ronan Curtis.
The visitors showed their attacking class once more when they again struck against the run of play as Ings squared for Cedric who smashed home from six yards.
A famous win for Saints was secured when Redmond weaved his way through blue shirts before hitting the net from distance as they inflicted a thrashing on their rivals.
What the managers said
Portsmouth boss Kenny Jackett: "It's a disappointing result, we needed the first goal. Some of our finishing wasn't quite there. We had a lot of chances but couldn't quite make the difference.
"We had momentum in both halves but the threat on the counter was big and in the end they made that count.
"The way they close and the way they pass is something we can learn from, and when they do get through they don't miss the target. The finishing was the big difference between the clubs tonight."
Southampton boss Ralph Hasenhuttl: "This is exactly the kind of game we needed. We had a first attack and a goal and it helped massively. Ings did a fantastic job today. I like it when players show me they want me to trust them. It's always a good atmosphere here, not easy to win. This is what we wanted to do.
"It was not a question to play a B-team, this was a massive game for us. We wanted to get to the next round."
Man of the match: Danny Ings
The forward proved the difference between the two sides with his expert finishing setting an example to his wayward Portsmouth counterparts.
What's next?
Southampton travel to North London to face Tottenham on Saturday, while Portsmouth look to kick-start their season against Bolton at Fratton Park.