Antonio Conte's side knew three points would be enough to finish fourth, and above rivals Arsenal, which they did that in emphatic fashion.
Arsenal did everything they could and thumped Everton 5-1 at the Emirates, but it was immaterial.
Any nerves Tottenham had were alleviated after just 16 minutes as Dejan Kulusevski to tap in from close range.
Harry Kane then put the visitors further ahead after 32 minutes, and equalled the record for most goals on the final day of the Premier League season (9) with Les Ferdinand and Andy Cole.
With Champions League virtually secured, the task then became trying to win the Golden Boot for Heung-min Son.
Kulusevski tried to play in Son when he had an open goal, but messed it up completely.
The on-loan Juventus forward added a second himself before the South Korea star netted twice to move to 23 Premier League goals for the season.
He ended up sharing the prize with Mohamed Salah, who scored a late goal for Liverpool against Wolves.
However, Son thanked his teammates afterwards in the changing room.
"Thank you so much for this unbelievable season and let's move on to the Champions League next season," before the others chanted his name in celebration.
Salah's celebration was a little more low key as Liverpool lost the Premier League title to Manchester City.
Hopes of winning four trophies were crushed by City's comeback against Aston Villa, though the Egyptian had a great season on a personal level.
He scored 31 times in all competitions with the Champions League final to come, and was recently voted the Football Writers' Association Footballer of the Year.
Salah also ended the campaign with 13 assists, which saw him secure the Premier League's Playmaker award in a double for the forward.