Moments after Victor Wanyama headed against the crossbar, Jose Fonte nodded home from Dusan Tadic’s corner to give Ronald Koeman’s men the lead in the 24th minute.
Seven minutes after the break, it was 2-0 as Tadic was involved again, this time linking up nicely with Cedric Soares before setting up Sadio Mane, who slotted the ball home from close range.
The result was wrapped up in the 73rd minute when the superb Tadic again provided an assist, this time finding Graziano Pelle who stroked it in to cap a good afternoon for the Saints.
Crystal Palace were undone by a second-half Steven Skrzybski double as they went down 2-0 away at Union Berlin.
The 22-year-old forward got the better of Wayne Hennessey in a one-on-one shortly before the hour mark, and he grabbed his second after a defensive mix-up from Palace.
West Ham earned a 3-2 win over Southend at Roots Hall in a spirited encounter with new signing Dimitri Payet the star of the show.
The Frenchman scored two superb goals and set up the third – an own-goal from Luke Prosser – in a virtuoso performance while Jack Payne and Kevan Hurst both netted for the home side.
Bournemouth battled back from a goal down against Exeter City to record a 2-1 win at Dean Court.
A first-half goal from David Wheeler gave the visitors the lead but Dan Gosling bundled home an equaliser in the second and Junior Stanislas won it late on with a superb strike from distance.
Swansea ended their pre-season tour of Germany with a 2-1 victory over 1860 Munich.
Jack Cork gave the Swans the lead in the seventh minute but Daniel Adlung’s penalty just after the hour mark levelled proceedings.
Substitute Bafetimbi Gomis secured victory for the Premier League side by firing home in the 73rd minute.
In the early hours of Saturday morning, Sunderland went down 3-1 to Pachuca in the second game of their tour of the USA.
Jack Rodwell fired the Black Cats in front early on, but Ariel Nahuelpan replied twice to put the Mexican side in front at half time, before Hirving Lozano added a third midway through the second half.