Former Liverpool manager Rafael Benitez's contentious reign as Everton boss got off to the perfect start as his side came from behind to beat Southampton 3-1.
The Spaniard, famous for a rather more high-profile comeback with the red half of the city in 2005, has plenty of work to convince the doubters he can ever be accepted at Goodison Park, but this was as good an opening as he could have wished for.
This was a performance which could have gone horribly wrong after Michael Keane's calamitous error had allowed Saints debutant Adam Armstrong to score his first Premier League goal midway through the first half.
Benitez's predecessor Carlo Ancelotti struggled throughout last season with a confidence problem at home, and in the period up to the interval that looked like being replicated.
However, Olympic champion Richarlison's golden touch got the hosts back on level terms early in the second half, Abdoulaye Doucoure's superb shot on the turn put them ahead and Dominic Calvert-Lewin's diving header clinched only the second win at Goodison Park since March.
Republic of Ireland captain Seamus Coleman started at right back for Everton.
Burnley 1-2 Brighton
Fellow Ireland defender Shane Duffy, who was on loan at Celtic last season, started for Brighton as they made a winning start to their campaign with late goals from Neal Maupay and Alexis Mac Allister seeing the Seagulls come from behind to beat Burnley 2-1 at Turf Moor.
Duffy's Ireland team-mate Aaron Connolly was not part of the Brighton matchday squad however.
Burnley took the lead via a second-minute James Tarkowski header, which stood after a VAR check amid Brighton claims that the defender had fouled Maupay, and the Clarets went on to rattle the woodwork twice before half-time, Johann Berg Gudmundsson hitting the post and Ben Mee the bar.
The visitors subsequently capitalised on those near-misses after the break as two substitutes helped them turn things around shortly after entering the fray, Jakub Moder teeing up Maupay's equaliser in the 73rd minute and Mac Allister then netting the winner five minutes later.
Ireland Under-21 cap Nathan Collins was on the bench for Burnley after his summer move from Stoke City.
Leicester 1-0 Wolves
Jamie Vardy scored a brilliant clinching goal as FA Cup winners Leicester City followed up their Community Shield victory over Manchester City with a narrow 1-0 win over Wolves.
The visitors, under new manager Bruno Lage, dominated the second half but could not match the exquisite finish by Vardy four minutes before half-time.
Vardy had been getting in behind the Wolves backline even before his brilliant goal.
He had a left-footed shot saved by Jose Sa in the 10th minute after Ayoze Perez's lofted pass into the left channel.
Then, after netting when clearly offside five minutes later, Leicester's 2020-21 top scorer tried a bold backheel after James Maddison's angled ball over the top.
Wolves, with Raul Jimenez leading the line intelligently on his first league appearance since fracturing his skull nine months ago, looked dangerous on the counter-attack, mainly through Adama Traore.
Five minutes before Leciester's goal, Joao Moutinho won possession in midfield and played a perfectly paced pass through the middle. Traore sprinted clear and set himself to sidefoot goalwards but shot just past the post.
Vardy made Wolves pay in style. Ricardo Pereira muscled his way past two men down the right wing and pulled a low cross to the near corner of the six-yard area where Vardy ran in front of Conor Coady to flick a brilliant left-footed shot past Sa.
Watford 3-2 Aston Villa
Watford record signing Ismaila Sarr starred on his Premier League return as the Hornets held off a late challenge from Aston Villa to secure a 3-2 win.
Sarr had already set up Emmanuel Dennis for his first club goal for Watford's opener before he found the net himself after an individual run down the right for his side's second.
Debutant Cucho Hernandez added the home side's third just moments after coming on but Aston Villa were able to reply through John McGinn's long-range effort.
In added time, referee Mike Dean pointed to the penalty spot after a foul in the box, with debutant Danny Ings stepping up and making no mistake for his new club, firing the ball into the back of the net.