Liverpool shrugged off a red card for Alexis Mac Allister on his Anfield debut to beat Bournemouth 3-1 on Saturday as Brighton thrashed Wolves 4-1 to go top of the Premier League.
Bournemouth had lost 9-0 on their visit to Anfield a year ago but could not have wished for a better start.
The Cherries had the ball in the net within seconds but Jaidon Anthony's tap-in was ruled out for offside.
Trent Alexander-Arnold's move into a midfield role resulted in a strong finish to a disappointing season for Liverpool last term, but he was guilty of giving the ball away for Antoine Semenyo's opener after only three minutes.
Liverpool needed some inspiration to kickstart their season after a 1-1 draw at Chelsea last weekend.
Luis Diaz provided it as he flicked up Diogo Jota's cross and then acrobatically fired an overhead kick into the bottom corner.
Jurgen Klopp's men led nine minutes before half-time, but Mohamed Salah needed a second opportunity to tap in the rebound after Neto had saved his penalty.
The Egyptian has now failed to score three of his last five penalties, including one when Bournemouth won the last meeting between the sides in March.
However, Salah's strike was enough to edge him ahead of Steven Gerrard as Liverpool's fifth highest scorer of all time on 187.
The momentum could have swung back Bournemouth's way when Mac Allister was harshly shown a straight red card for leading with his studs on Ryan Christie, despite minimal contact with the Scotland international.
But the 10 men added to their lead within four minutes when Jota pounced after Neto could only palm Dominik Szoboszlai's effort into his path.
Japan captain Wataru Endo was then introduced after Liverpool finally landed a defensive midfielder on Friday after losing out on Moises Caicedo and Romeo Lavia to Chelsea.
- Seagulls soar -
Brighton banked a British record transfer fee that could rise to £115 million for Caicedo on Monday.
But the Seagulls continue to soar under Roberto De Zerbi despite seeing their best players picked off by the Premier League's elite.
Kaoru Mitoma may be the next big-money departure and the Japanese international opened the scoring in stunning style at Molineux as he slalomed past four Wolves defenders before producing a classy finish.
Wolves had thoroughly outplayed Manchester United despite losing 1-0 at Old Trafford on Monday.
But they had no answer to Brighton's speed of passing and movement as the visitors scored three times in the first 10 minutes of the second half.
Mitoma teed up Pervis Estupinan to smash home for 2-0 before Solly March scored twice from Julio Enciso assists.
Wolves pulled a goal back through Hwang Hee-chan, but a chastening afternoon for Gary O'Neil's men wiped away the optimism surrounding their performance at United.
Brentford are also making light of the absence of the suspended Ivan Toney as they won 3-0 at Fulham.
Yoane Wissa pounced on an error from Issa Diop to open the scoring just before half-time.
Bryan Mbeumo doubled the Bees' lead from the penalty spot after Fulham captain Tim Ream was sent off for a second yellow card.
Mbeumo then rounded off the scoring in stoppage time to lift Brentford up to second.
Tottenham aim to get the Ange Postecoglou reign up and running later when they host Manchester United in their first home game since the departure of Harry Kane.
Champions Manchester City are in action at 1900GMT when they host a Newcastle side that began the day on top after a 5-1 thrashing of Aston Villa on the opening weekend of the season.
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