Sadio Mane's hat-trick was scored in two minutes and 56 seconds, which is a Premier League record.
The six goals mean that the Saints have scored 37 times at home this season - only Manchester City and Manchester United have better returns.
As for Villa, Christian Benteke headed in his 15th goal of the season.
Burnley 0-0 Stoke City
Stoke's return of 51 points is their best ever return in a Premier League season.
The hosting Clarets scored just 14 goals in 19 outings at Turf Moor - fewer than any other side has managed at home.
Sean Dyche's men have found the net just once in their last eight matches.
Queens Park Rangers 2-1 Newcastle United
The home side recorded their first victory over Newcastle since 1995.
The Magpies have now collected just one point from the last 30 that have been on offer.
Striker Emmanuel Riviere scored his first goal for Newcastle, which ended a drought of 1,084 minutes for the Frenchman.
Sunderland 0-0 Leicester City
Leicester were bottom at the beginning of April, but this point secured their Premier League status.
The Black Cats have drawn eight of their home matches this term - a Premier League high.
Sunderland midfielder Lee Cattermole was booked for the 14th time this term, which equals the record held by Robbie Savage, Mark Hughes and Cheick Tiote.
Tottenham Hotspur 2-0 Hull City
Nacer Chadli's goal in the 54th minute was scored with the game's first shot on target.
Spurs have lost none of their last seven Premier League meetings with Hull.
As for the Tigers, they still have not won a Premier League match in the month of May, drawing three and losing nine.
West Ham United 1-2 Everton
The Hammers have won just two of their last 15 Premier League games.
It appears that Romelu Lukaku enjoys playing against West Ham, having scored his sixth goal in as many appearances against them.
Everton midfielder Gareth Barry was booked for the 104th occasion in the Premier League.
Liverpool 1-3 Crystal Palace
On what was his final home appearance before leaving for the MLS, Steven Gerrard completed 90 minutes at Anfield for the first time since January 1.
Visiting Palace won away at the red half of Merseyside for just the second time in their history.
Second-half substitute Wilfried Zaha scored just 23 seconds after he had entered the action.
Swansea City 2-4 Manchester City
Manchester City carried on their recent good form, with this being their fifth victory on the bounce.
Ivorian midfielder Yaya Toure scored twice, the first of which took his Premier League goal tally to 50.
Swansea striker Bafetimbi Gomis scored his fifth goal in as many outings.
Manchester United 1-1 Arsenal
Ander Herrera's goal was the first that Arsenal have conceded in the first half of a Premier League match since New Year's Day.
It was the Spanish midfielder's eighth goal of the season in all competitions for United.
Meanwhile, Arsenal manager Arsene Wenger named the same starting lineup for the sixth game running.
West Bromwich Albion 3-0 Chelsea
Blues midfielder Cesc Fabregas was red-carded for the second time in his Premier League career, with his first coming back in 2006.
West Brom striker Saido Berahino scored a brace, taking his goal tally for the season in all competitions to 20.
The victory was the first that the Baggies had secured over the West Londoners in five attempts.
