Liverpool ensured a return to the Champions League by beating relegated Middlesbrough, although they will have to play in a qualifying round after finishing fourth in the Premier League, two points behind Manchester City.
Arsenal failed to qualify for the Champions League for the first time in 20 years to renew scrutiny of Arsene Wenger despite a 3-1 victory over Everton on Sunday.
Liverpool fans had reason to be anxious, having not forgotten three years ago, as Everton were deemed to have put in a lax performance at Goodison Park, losing 3-2 to Liverpool's then title rivals Manchester City.
However, despite being beaten on the last day, events during a one-week period earlier in the season certainly helped Liverpool beat Arsenal to fourth thanks to some help from their rivals.
The Dutchman loves a goal in a big game and with a spot under the bright lights at stake he ran on to Roberto Firmino's clever pass before arrowing a shot past Middlesbrough 'keeper Brad Guzan late in first half stoppage time.
But the puzzle of top-four finishers had always been solved as goals from Georginio Wijnaldum, Philippe Coutinho and Adam Lallana calmed palpable tension at Anfield.
Liverpool will be back in the Champions League next season, though they will have to play in the playoff round to reach the group stage. Wenger didn't even join in, remaining on the touchline with his arms folded.
Gabriel was stretchered off in the second half at the Emirates with an apparent knee injury and with Shkodran Mustafi absent here due to illness, it leaves Wenger facing a selection crisis in defence.
Terry came off in the 26th minute - his shirt number - as his teammates formed a guard of honour for the 36-year-old defender, who left the pitch to a standing ovation. Chelsea's 30th win of the campaign was sealed by Eden Hazard, Pedro Rodriguez and a double from Michy Batshuayi.
On his ambitions for the close-season transfer window, Koeman said: "First of all we need more numbers in to be prepared for a long, tough season with different competitions". It brought his tally for the season to 29. Dele Alli, Victor Wanyama, Ben Davies and Toby Alderweireld also netted for Tottenham.
Jose Mourinho named Manchester United's youngest ever Premier League starting line-up, with an average age of 22 years and 284 days, and the kids rose to the occasion with a 2-0 win over Crystal Palace.
They had not won in their three previous games at Anfield.
The draw for the play-offs will take place on August 4.
It has done so amid the most intense competition: It is unheard of for a team to miss out with the 75 points Arsenal gathered.
Sean Dyche has also impressed by leading Burnley to its highest league position since 1975. Southampton, on the other hand, accrued just six more points than Watford, which finished 17th. No season in football always goes up; there are dips too.
On whether uncertainty over his future affected Arsenal's form... However, the way Chelsea set about the closing matches of the season was testament to both the new-found team-spirit and the work ethic installed by the Italian, whose positive personality looks to have been key to success.
- LeBron James not interested in this reporter's question following Game 3
- Preakness 2017 runner-up Classic Empire Belmont Stakes-bound
- WannaCry Is the Ransomware Attack We Should Have Been Ready For
- La Liga win is bigger than World Cup-Zidane
- Chelsea Manning released after 7 years in military prison
- Horschel defeats Day on first hole of playoff
- Trump warns ex-FBI director Comey about 'leaks' in explosive Twitter rant
- Royal Mo suffers fracture during workout
- Rested and ready: 13-1 shot Cloud Computing wins Preakness
- Australian reportedly dies on Mt Everest