Ronald Koeman's side claimed a comfortable victory to remain hot on Liverpool's heels, while the result leaves the Villains at the heart of the relegation battleSadio Mane scored the fastest hat-trick in Premier League history as Southampton beat Aston Villa 6-1 to boost their Europa League hopes and keep the visitors looking nervously over their shoulders.
Villa knew victory at St Mary's Stadium would have secured their top-flight status, but Tim Sherwood's men were left stunned by Mane's record-breaking treble, which came in just two minutes and 56 seconds.
It shaved 97 seconds off the record set by Robbie Fowler for Liverpool in 1994 and effectively ended the game as a contest inside the opening 16 minutes.
Yet there was more punishment to come for relegation-threatened Villa, with Shane Long netting a tap-in and a superb long-range strike.
Christian Benteke's header on the stroke of half-time did little to lighten Sherwood's mood, with FA Cup finalists Villa still heading in disconsolate at the break.
Villa navigated the second half with only a Graziano Pelle goal against them but their Premier League status was confirmed later in the day after Hull City lost to Tottenham, while Southampton's European prospects now look much brighter.
The hosts were denied an early opener when Pelle was incorrectly flagged for offside, having timed his run well before slotting past Shay Given.
Benteke was presented with an excellent opportunity to put Villa ahead in the 12th minute, but the Belgium striker toe-poked his effort wide after collecting Fabian Delph's throughball inside the box.
He was made to rue that miss when Mane started his scoring spree a minute later, collecting the loose ball and slotting home after his own shot was saved.
Villa were the architects of their own downfall for the second as Ron Vlaar's backpass found Long, whose shot was saved by Given but fell kindly for Mane to convert.
Incredibly, Mane was not done there and took his league goals tally to 10 for the season when he found the top-right corner from Long's cut-back.
Having played such a key role in helping his team-mate make history, Long then took centre stage himself, first tapping in from Pelle's saved shot and then curling a glorious shot over the stranded Given from 25 yards.
Benteke cut the deficit with a towering header in first-half stoppage time, though Sherwood remained unmoved in the dugout at the end of an abysmal 45 minutes for his side.
Ronald Koeman's men hit Sunderland for eight in October, but there was to be no repeat as Villa showed some defensive resolve after the interval.
Long flashed a volley wide on the hour mark in a second half when Southampton understandably lacked urgency, while Villa's focus on damage limitation curbed their attacking threat.
Substitute Maya Yoshida saw his late header brilliantly kept out by Given, while Nathaniel Clyne fired over before Pelle's volley put the gloss on things.
Villa's attentions will now turn to hosting already-relegated Burnley on the final day in the hope they will not be facing them again next season, while Southampton head to Manchester City in pursuit of a top-six finish.