Newly promoted, Fulham held title contenders Liverpool to a sluggish draw at the weekend in the opening week of the Premier League season, while Arsenal got off to a flying start on Friday and Tottenham delivered on its pre-season hype by thrashing Southampton as Chelsea struggled to scrape a win.
Liverpool had to come from behind twice to cancel out goals from Fulham's Serbian striker Aleksandar Mitrovic with new signing Darwin Nunez and Mohamed Salah on target in the 2-2 draw for Jürgen Klopp's side.
Spurs also went behind, at home to Southampton, but then Antonio Conte's side cruised to a 4-1 victory over the Saints.
A penalty on the stroke of halftime from Jorginho was enough to give Chelsea a hard-fought 1-0 win at former favorite Frank Lampard's Everton.
Champions Manchester City starts their title defense at West Ham United on Sunday while Dutch manager Erik ten Hag takes charge of Manchester United for the first time against Brighton & Hove Albion at Old Trafford.
Mitrovic scored 43 goals in 44 games as Fulham won promotion from the second-tier Championship last season and continued that form as he put the London side ahead in the 32nd minute.
Kenny Tete's cross from the right was just what the tall center forward relishes and he out-muscled Trent Alexander-Arnold at the far post to head home.
Runners-up last term, Liverpool struggled to get a foothold in the game but the introduction of Nunez in the second half had the desired impact.
The Uruguayan, bought from Benfica for an initial fee of 75 million euros ($76.36 million) brought the visitors level with a clever flicked finish just after the hour mark.
Despite having barely threatened after the break, Fulham were soon back in front as Mitrovic was ruled to have been tripped in the box by Virgil van Dijk, and the Serb stepped up to stroke home the spot kick to make it 2-1.
If signing Nunez was Liverpool's highest-profile move in the market, the new contract for Salah is arguably their most significant piece of business and the Egyptian showed his value again poking home the equalizer from close range.,
Debutants boost Arsenal
Arsenal battled to beat Crystal Palace 2-0 on Friday, with Gabriel Martinelli scoring the first goal before home defender Marc Guehi turned the ball into his own net late on at Selhurst Park.
Arsenal striker Gabriel Jesus, who arrived from Manchester City in the close season, looked set to get off to a flying start by dancing through the Palace defense only to see his shot blocked, with Martinelli dragging the rebound wide of the post.
Oleksandr Zinchenko, another new signing from City, also looked lively and had an early shot blocked as Arsenal quickly raised the tempo but the Ukrainian soon had a hand in the opening goal as Palace were caught flat-footed at a corner.
Bukayo Saka's inswinger found Zinchenko in acres of space and he headed the ball back across goal where Martinelli was on hand t nod it into the net.
Palace could have leveled before the break as Odsonne Edouard headed goalwards, but visiting goalkeeper, Aaron Ramsdale pulled off a superb reflex save to preserve his side's lead.
Sensing they might snatch a draw, Palace coach Patrick Viera threw everyone forward for the last 15 minutes but the visitors doubled their lead when Saka's cross was deflected into his own goal by Guehi in the 85th to seal the points for the away side.
"We started really sharp ... to win here you need to suffer," Arsenal manager Mikel Arteta told Sky Sports. "We've done it and that's part of the mentality that we want to build, to come to these places and find a way to win,"
French defender William Saliba was outstanding for Arsenal as he finally made his debut after three years spent on loan at different clubs in France.
"We knew it would be hard here but we were strong and solid," the 21-year-old said. "I've waited a long time to make my debut and I'm happy to start with a clean sheet and a win, it's important for confidence."
Impressive start
Tottenham's close-season recruitment has boosted hopes in north London that Antonio Conte's side can get closer to the top two this season and they confirmed that positive perspective with an impressive start.
The hosts fell behind to a James Ward-Prowse volley in the 12th minute but dominated throughout with goals by Ryan Sessegnon, Eric Dier and Dejan Kulusevski sealing the win.
Southampton's lead lasted only nine minutes before Sessegnon powered a header past Premier League debutant goalkeeper Gavin Bazunu from Kulusevski's cross.
Dier glanced in Son Heung-min's cross with a stooping header in the 31st minute to put Tottenham ahead, and the hosts should have been out of sight before the interval.
Mohammed Salisu clumsily turned Emerson Royal's cross into his own net in the 61st minute, and two minutes later Royal set up the impressive Kulusevski to guide an exquisite finish beyond Bazunu whose saves kept the score respectable.
Chelsea peppered Everton's goal with 13 corners in the first half but looked set to be frustrated as the interval approached, only for Jorginho to convert from the spot after Ben Chilwell had been fouled to give the visitors the lead.
A brilliant save from Edouard Mendy early in the second half to deny Abdoulaye Doucoure preserved Chelsea's advantage, and that was as good as it got for a disappointing Everton, who only survived relegation by the skin of their teeth last term.
England forward Raheem Sterling, making his first league appearance for Chelsea after a summer switch from Manchester City, could have marked an impressive debut with a late second but saw his close-range effort deflected just wide.
Nottingham Forest's return to the top flight after a 23-year absence ended in a 2-0 loss at Newcastle United with Fabian Schar scoring a screamer before Callum Wilson sealed the win.
There was a better start for another promoted side, Bournemouth, who beat Steven Gerrard's Aston Villa 2-0 with goals from Jefferson Lerma and Kieffer Moore.
Leeds United, who battled against relegation last season, had a new look with four debutants and enjoyed a 2-0 win at home to Wolverhampton Wanderers.