Manchester City were confirmed champions with three rounds of fixtures left.
Liverpool, meanwhile, have still not secured a place in the Champions League next season - despite reaching this year's final.
Ayoze Perez scored twice after Dwight Gayle's opener to ensure Rafael Benitez's Newcastle finished an impressive 10th in the table, while Antonio Conte's side had to settle for fifth and a shot at the FA Cup in Saturday's final against Manchester United. Swansea took the lead against Stoke but fell to a 2-1 defeat and a place in the Championship next season.
"They have been with us all season".
Record-breaking City end season on a high Rarely has City boss Pep Guardiola celebrated a goal like he did when Jesus' exquisite 93rd-minute chipped finish hit the net. We give them two days and then go to a camp.
Pak Terrorists behind 26/11 attacks: Ex Pak PM Sharif
In comments published today by the Pakistani daily Dawn , the ousted leader asked, "Militant organisations are active". Pakistan's economy could have been grown at 7% annually, but it was struggling to get there, Sharif said.
A plane flew over the stadium, carrying the message "Merci Arsene, we will miss you too" in response to Wenger's goodbye speech last week at the Emirates Stadium.
City were desperate to bring up 100 points despite clinching the Premier League title four weeks ago but had to wait until the final moments of the season to achieve it.
Their victory on the road at St Mary's also means they have recorded more away wins (16) and collected more away points (50) than any other team, with Jose Mourinho's Chelsea side in 2004-05 the previous record holder.
Swansea paid tribute to long-serving custodians Angel Rangel and Leon Britton before kickoff. They also were level at 4 following Jamie Vardy's second of the night when Kane completed his brace.
As well as hitting 100 points, City's 32nd win broke Tottenham's 57-year-old record for victories in a single top-flight campaign.
"Do I feel relief?" The Baggies couldn't stand as firm at Crystal Palace, though, losing 2-0 after second-half goals from Wilfried Zaha and Patrick van Aanholt.