Both were given scares, but after Liverpool had scored late to beat Newcastle United 3-2 on Saturday night, Man City responded with a narrow 1-0 triumph over Leicester City on Monday to leave just one point in it with one game left.
The destination of the trophy is the only major thing to be decided on the final day after the top-four race was all but wrapped up, with Chelsea now guaranteed Champions League football next season courtesy of their win over Watford.
Tottenham Hotspur still have work to do after they had two men sent off en route to defeat against Bournemouth, but it would take results to go drastically against them - including a major swing in goal difference - if they were to be caught by Arsenal following the Gunners' draw at home to Brighton & Hove Albion.
Wolverhampton Wanderers are guaranteed 'best of the rest' status in seventh and must now wait for the FA Cup final to discover whether they will be in Europe next season, with Everton unable to catch them despite their win over Burnley.
Here, Sports Mole selects its Premier League team of the week from the penultimate gameweek of the season.
One Premier League appearance, one selection in the team of the week. Mark Travers became the youngest Premier League goalkeeper since October 2006 for Bournemouth on Saturday, and marked the occasion with a string of fine saves to keep Tottenham at bay. The story of the game went on to become Spurs' two red cards, but the 19-year-old made five stops and was named man of the match.
The match-winner in that game was Nathan Ake, who played in a more advanced midfield position but is chosen at centre-back for us this week ahead of the likes of Virgil van Dijk, Shane Duffy, Lewis Dunk, Kurt Zouma and David Luiz.
The story of the entire Premier League season may boil down to Vincent Kompany's unexpected rocket against Leicester, with the Man City skipper once again stepping up when their side needed a hero. Leicester were looking solid against Man City's attacks until Kompany fired his goal-of-a-lifetime in off the underside of the bar - one that will prove to be an iconic moment in the competition's history should City complete the job on Sunday.
West Ham's win over Southampton earns them four representatives in this XI, including both full-backs. Ryan Fredericks was particularly impressive - not only for his goal but also in making four tackles and winning and game-high 10 aerial duels - while Arthur Masuaku on the opposite flank was also an important presence both in attack and defence.
An honourable mention must go to Trent Alexander-Arnold - who made the most of a red card reprieve to add two more assists to his tally - while the likes of Matt Doherty, Seamus Coleman, Lucas Digne and Matt Ritchie were also under consideration for the full-back roles.
The Hammers duo are joined in the team by their skipper Mark Noble, who ran the show against Southampton and helped himself to an assist as well. There was once again plenty of competition for the midfield positions, including from Noble's clubmate Pedro Obiang, but it was the Englishman who made things tick in one of the more impressive team performances of the weekend.
Morgan Schneiderlin, Wilfred Ndidi and James McArthur were also in contention, but Ruben Loftus-Cheek joins Noble in this XI having made a big impact off the bench for Chelsea after replacing the injured N'Golo Kante. The England international carried the ball well and opened the scoring for the Blues as they broke clear in the second half.
As is often the case, Eden Hazard was the main star in that Chelsea win, marking what could be his final home league appearance for the club with a couple of assists to take him up to 15 for the season - more than any other player in Europe's top five leagues.
Hazard finds himself in the number 10 role for this XI, alongside Ryan Fraser and Andros Townsend. Fraser's scampering runs were instrumental in taking the fight to nine-man Spurs during Bournemouth's surprise win - not to mention delivering the corner which provided the winner - while Townsend helped himself to a goal and an assist in Crystal Palace's triumph over Cardiff.
Marko Arnautovic leads the line to complete the West Ham quartet having finally broken his scoring drought, netting twice for his first goals since January as he looked to be back to his best. The Austrian just about edges Salomon Rondon to a place in the team, while mentions should also go to Gonzalo Higuain, Wilfried Zaha and Pedro.