Last season's Premier League top scorer Mohamed Salah was on target again as Liverpool began their campaign with an easy 4-0 win at home to West Ham United.
The Egyptian gave Juergen Klopp's side the lead after 19 minutes from Andy Robertson's precise low cross.
Later in the evening, Manchester City, who romped to Premier League success by 19 points last season, began the defence of their title with an impressive win away to an Arsenal side playing under new Spanish manager Unai Emery.
Attempting to become the first team since Manchester United in 2009 to retain the title, the champions were good value with goals by Raheem Stirling and Bernardo Silva.
West Ham's new manager Manuel Pellegrini gave debuts to five of their 10 close-season signings, but his revamped team rarely threatened Liverpool's expensive new Brazilian goalkeeper Alisson.
Poor defending cost them a second goal just before the interval, to Sadio Mane, who added a third after 53 minutes from an off-side position.
Substitute Daniel Sturridge made it four just seconds after coming on.
Salah's goal featured an important contribution from new signing Naby Keita, who cost 50 million pounds ($63.84m) from RB Leipzig.
Guinea's Keita was excellent throughout. Liverpool's other debutant, Alisson, was much less involved as the London side struggled to make chances.
Their best one followed a lucky bounce off the referee but Marko Arnautovic miscued his shot.
By the interval they had conceded again after leaving three attackers unmarked in front of goal. Mane was the one who knocked in James Milner's pull-back.
He scored Liverpool's third, which might have been disallowed for offside, and Sturridge came off the bench in the final few minutes to score at the far post from a corner with his first touch.
The result continued West Ham's dreadful record at Anfield, which now extends to one win in 46 league games. Liverpool, meanwhile, have not conceded a goal in their last six home games in the league -- since West Ham scored against them in February.
Pellegrini gave debuts to Lukasz Fabianski, Ryan Fredericks, Fabian Balbuena, Felipe Anderson and Jack Wilshere, then introduced a sixth newcomer Andriy Yarmolenko as a substitute.
Anderson and Yarmolenko had their moments but overall the visitors were comprehensively outplayed.
Champions City impressive winners at Arsenal
Sterling went past two weak challengers to put City ahead in the first quarter of an hour with his 50th league goal.
Soon after debutant Riyad Mahrez from Leicester City was substituted, Bernardo Silva added the second in the 65th minute.
Defender Sokratis Papastathopoulos and teenage French midfielder Matteo Guendouzi made their Arsenal debuts but like so many teams last season the London side found City hard to cope with.
Another new signing, Stephan Lichtsteiner from Juventus, had to replace full back Ainsley Maitland-Niles before the interval and in the second half Uruguayan Lucas Torreira, who is expected to become an important defensive midfielder, also came on.
Pierre-Emerick Aubameyang, who finished last season with four goals in three games, had few chances and Alexandre Lacazette wasted one within a few minutes of coming on in the second half.
City's strength in depth was illustrated when Mahrez made way for Kevin de Bruyne just before the hour mark.
Soon afterwards Sergio Aguero was guilty of shooting instead of playing in De Bruyne but in the next attack Benjamin Mendy, making his first league start since last September, set up Bernardo Silva to score.
City have now lost only one away game in the league -- at Liverpool -- of their last 21.
"I think we were better than them today," Bernardo Silva told Sky Sports. "We wanted to be professional and we did it. We defended very well and were a very compact team."
Emery, meanwhile, will know he has much to do, even before a difficult derby with Chelsea next weekend.