Laurent Koscielny scored a 52nd-minute winner as Arsenal won 1-0 at Newcastle United to secure fourth place with 73 points, one point ahead of fifth-placed Spurs who mustered a late goal from Gareth Bale to beat Sunderland 1-0 at White Hart Lane.
"These players are special, I told them many times, they showed it in the last two months they have been absolutely exceptional," Arsenal manager Arsene Wenger, whose side had trailed Spurs by seven points in March, told Sky Sports.
Chelsea sealed third place on 75 points with a 2-1 win at home to Everton, where both Rafael Benitez and David Moyes were taking charge of their sides for a final time.
Manchester United had already been crowned champions and their attention was on giving retiring manager Alex Ferguson a send-off to remember but as the goals rained in they could not give him a win as they drew 5-5 at West Bromwich Albion.
Last year's champions Manchester City finished 11 points behind United in second after a 3-2 defeat at home to Norwich City on a day where 36 goals were scored across the 10 fixtures.
With first and second place decided some time ago and all three relegation spots already determined, the burning issue of the day centred on who would grab the final top-four place.
Discounting the highly improbable mathematical possibilities, it boiled down to a battle between north London's big foes Arsenal and Tottenham.
Arsene Wenger's side had the advantage before kickoff, with a one-point lead and the knowledge that as long as they won at Newcastle, the Champions League place was theirs.
They were facing a Newcastle side who were no longer troubled by relegation fears after securing their top-flight status and that lack of pressure translated into a troublesome first half for Arsenal as the hosts enjoyed the better chances.
Arsenal came out for the second half with a bit more spark and seven minutes into it finally got the goal they craved as Theo Walcott's free kick was headed on by Per Mertesacker and Koscielny stayed onside to prod the ball home.
Walcott hit the post in stoppage time as Arsenal ended a nervy game on top.
At White Hart Lane, Spurs had more urgency about them from the outset than Arsenal but were left questioning referee Andre Marriner's decision to book Bale for diving.
Bale, who has picked up a series of player of the year accolades this season, was shown the yellow card midway through the first half although television replays showed Seb Larsson's foul could have led to a valuable Spurs penalty instead.
With news filtering through that Arsenal had gone ahead in their game, Andre Villas-Boas' side continued to press for an opener with Michael Dawson, Bale, Scott Parker and Aaron Lennon among those going close.
They were given some hope with 15 minutes to go when Sunderland's David Vaughan was sent off after a second yellow and finally made the man advantage count as Bale curled in a stunning goal on 89 minutes.
HIGH SCORING
But it was not enough for Spurs who missed out on Europe's elite club competition for the second year running.
Spurs finished fourth last season behind Wenger's side but they were denied a Champions League berth because sixth-placed Chelsea took the final spot as European champions.
In 2006 they were also pipped by Arsenal after many Spurs players were hit with food poisoning before their game with West Ham United.
If they had won that game they would have secured fourth, but they lost and Arsenal overtook them.
"It is difficult to take, in the end we did what we had to but Arsenal did their job well and go through. It is difficult at this moment," Villas-Boas told Sky Sports.
Away from the frantic battle for fourth place, the only real need for a calculator was to keep track of the number of goals on a high-scoring day.
None more so than at The Hawthorns, where having secured a 20th league title with four games to spare, Manchester United's trip to West Bromwich Albion was little more than an opportunity to say farewell to Ferguson.
United had established a three-goal lead by the half-hour mark through Shinji Kagawa, an own goal from Jonas Olsson and an effort from a tight angle by left back Alex Buttner, making a rare start.
They were not going to have it all their own way in Ferguson's 1,500th and final game, however, as James Morrison got West Brom on the scoresheet five minutes before the break and Romelu Lukaku pulled another goal back on 50 minutes.
United resumed control as top scorer Robin van Persie netted his 26th league goal of the season from a low cross from Antonio Valencia on 53 minutes, while Javier Hernandez scored the fifth 10 minutes later after a cross from substitute Ryan Giggs.
West Brom had not read the script though as they scored three times in five minutes towards the end of the game, with Lukaku completing a hat-trick and Youssouf Mulumbu also finding the net, as Ferguson was denied the win he had so wanted.
'WE FORGIVE YOU'
His successor at Old Trafford, Moyes, could also not sign off with a victory in his final game in charge of Everton as hosts Chelsea made sure of an automatic passage into the Champions League group stage with third place.
Chelsea went ahead in the seventh minute through Juan Mata before Everton pulled one back seven minutes later with a good Steven Naismith finish.
The Europa League winners sealed the three points when Fernando Torres fired home at the near post for his first league goal of 2013 as Benitez left having won over some of the club's critical fans. One even held up a banner saying "we forgive you".
Manchester City ended a disappointing season, where they lost the FA Cup final to relegated Wigan Athletic and gave up their Premier League title without much of a fight, on a losing note at home to Norwich.
They had twice come from behind with goals from Jack Rodwell to draw level before Jonathan Howson won the game for the visitors on 65 minutes.
There were six goals at West Ham as Kevin Nolan scored a hat-trick in the hosts' 4-2 win over Reading, who had already been consigned to second-tier football for next season along with Wigan and Queens Park Rangers.
QPR bid goodbye to the top flight with a 1-0 defeat at Liverpool where Anfield favourite Jamie Carragher was making his final appearance before retirement, while Wigan drew 2-2 at home to Aston Villa.
Elsewhere, Fulham beat hosts Swansea City 3-0 and Southampton drew 1-1 at home to Stoke City.
