Meanwhile, Manchester City moved to third with a win at home to Crystal Palace
Manchester City flexed their attacking muscle this afternoon in the Premier League to move third in the table.
Their 5-0 win at home to Crystal Palace dislodged Liverpool and leaves them still in with a very slim chance to finish in second ahead of Tottenham.
Hull City missed their chance to move clear of the relegation zone, and ended the day in the bottom three after slipping to a 2-0 defeat to already relegated Sunderland at the KCOM.
It was their first defeat at home under manager Marco Silva. Before today they had won six from their seven home games under their new manager.
There were draws for West Brom away to Burnley and Bournemouth had to come from behind twice to earn a point at home to Stoke City. It finished 2-2 in each of those games.
Elsewhere, Leicester City officially secured their Premier League status with a 3-0 win at home to Watford.
In the day's late game, Swansea picked up a crucial 1-0 win at home to Everton to move out of the relegation zone.
Hull City missed their chance to move five points clear of Swansea City in the relegation zone as they slipped to a first home defeat under Marco Silva.
A win against already relegated Sunderland would have moved them to within a point of 16th place Crystal Palace and would have handed them the momentum heading into the final two games of the season.
Palace's heavy defeat to City before kick-off today was all the incentive Hull needed, but failed to make up ground on their London opponents.
The pair now come head-to-head next week at Selhurst Park and a loss, coupled with a Swansea victory over Sunderland, would see them relegated. They slip into the relegation zone after Paul Clement's side result against Everton.
Today could prove to be a costly, costly defeat.
Jermain Defoe celebrates scoring Sunderland's second goal of the afternoon at the KCOM Stadium. Image: Dave Howarth/PA Wire/PA Images
Manchester City can still finish in second, but at this stage in the season, will happily take a Champions League place in third.
With their cross-city rivals Manchester United closing in on a spot in Europe's premier club competition via the Europa League, Pep Guardiola will go head-to-head with Jurgen Klopp in the battle for third.
They sent a message to the Reds this afternoon in the day's early game - a rampant 5-0 win over strugglers Crystal Palace. With games remaining against West Brom, Leicester and Watford, Guardiola will expect a strong finish from his side to hold onto a place in the top three.
Leroy Sane starred as Manchester City ran riot against Crystal Palace. Image: Mike Egerton/PA Wire/PA Images
Swansea will have looked on today's action at the KCOM Stadium with glee. Hull City - their primary relegation rivals - dropping points at home to an already relegated Sunderland side.
What a time to pick up their first home loss under Marco Silva. Coming off the back of a hard-fought point away to Manchester United last weekend, the Welsh side then picked up maximum points against Everton in front of their home fans.
With results like that, you tend to forget that Paul Clement is their third manager this season and that for so long this season they faced turmoil in the top flight. Summer signing Fernando Llorente got the only goal of the game at the Liberty Stadium for Swansea and they know they can secure their top flight status next weekend against Sunderland - other results depending.
The great escape could be confirmed as soon as next week.
Fernando Llorente got the only goal of the game this afternoon as Swansea beat Everton. Image: David Davies/PA Wire/PA Images