Virgil van Dijk then restored the home side’s advantage with a header from a corner before the Dutch defender went from hero to villain with an error that allowed Patrick Bamford to score at the Kop end.
Salah then thundered his second of the evening into the top corner – and the Reds’ 550th goal under Jurgen Klopp - to cap a sensational opening 33 minutes of football.
Inevitably, the second half couldn’t quite live up to the rollercoaster nature of the first, but it remained end to end and Leeds reached parity once again when Mateusz Klich burst into the box and fired a sweet shot beyond Alisson on 66 minutes.
Liverpool pressed for a winner and got it two minutes from time. Salah claimed the match ball with another clinical penalty as the Merseysiders extended their unbeaten league run at Anfield to 60 matches.
Klopp’s men will now turn their focus on a visit to big-spending Chelsea on Sunday while Leeds have a midweek EFL tie with Hull prior to their first Premier League home game against Fulham on Saturday.
Mohamed Salah of Liverpool celebrates with Roberto Firmino after scoring his team's third goal during the Premier League match between Liverpool and Leeds United at Anfield on September 12, 2020 in Liverpool, England
Image credit: Getty Images
An Anfield thriller as Leeds’ return ends in heartbreak. This was a perfect advert for the Premier League. It was packed with incident as two sides committed to attacking went toe-to-toe in a pulsating clash of champions.
For Liverpool the areas they need to address are clear if they are to go on and achieve their dream of retaining the title. The defence looked porous with even the usually reliable van Dijk appearing suspect. They need to tighten up and cut out errors that were creeping in during the final rounds of matches last term. However, the forward line remains one of the most feared around, with Salah in particular getting them out of trouble here. The Reds have made a habit of finding a way in the last few years and it was perhaps no surprise to see them do it again.
Leeds gave an outstanding account of themselves on their long-awaited return to the big time. Marcelo Bielsa and his players will get plenty of plaudits after this display but the reality is they didn’t get the point they will feel they deserve. Some weak defending at set pieces and naivety for the late penalty proved costly, but they showed enough to suggest they can enjoy a relatively successful campaign and will win fans along the way.
MAN OF THE MATCH
Mohamed Salah (Liverpool). The Reds forward was razor sharp. He was ice cool with his penalties and lethal with his second goal of the day. Most of Liverpool’s best moments in attack involved him and he was clearly crucial to the home team's victory.
LIVERPOOL: Alisson 6, Alexander-Arnold 5, Gomez 5, Van Dijk 6, Robertson 6, Henderson 6, Wijnaldum 6, Keita 6, Salah 8, Firmino 7, Mane 7. Subs: Fabinho 6, Jones 6, Matip n/a. LEEDS UNITED: Meslier 7, Ayling 6, Koch 6, Struijk 7, Harrison 7, Klich 7, Dallas 7, Phillips 7, Costa 7, Hernandez 6, Bamford 7. Subs: Roberts 6, Rodrigo 5, Shackleton n/a.
4' - Liverpool 1-0 Leeds. Salah rifles an early penalty straight down the middle to get the Reds off to a flyer. The spot kick was awarded after Leeds debutant Koch was penalised for blocking the Egyptian’s initial shot with his hand.
12' - Liverpool 1-1 Leeds. The visitors are level! Jack Harrison races on to a diagonal ball, weaves beyond Alexander-Arnold and Gomez before drilling a low shot into the corner.
20' - Liverpool 2-1 Leeds. Van Dijk restores the home side's advantage with a powerful header from Robertson's left-wing corner.
30' - Liverpool 2-2 Leeds. Bamford clips a clever finish beyond Alisson after a howler from van Dijk.
33' - Liverpool 3-2 Leeds. Liverpool are back in front. Salah takes down a half cleared free kick and slams it into the top corner from the right side of the area.
66' - Liverpool 3-3 Leeds. Wow - it's 3-3! Klich takes a pass on the run into the box and volleys a sumptuous shot into the far corner.
88' - Liverpool 4-3 Leeds. Salah slams in his hat-trick from the spot with a cool finish into the corner after Rodrigo tripped Fabinho in the box.
Salah is the first ever Liverpool player to score on the opening day of four consecutive league seasons; he's only the second to do so in the PL for any club, after Teddy Sheringham (1992-93 to 1995-96).
Harrison is the first player to score on his Premier League debut for Leeds since Nick Barmby in August 2002 vs Man City, and the first to do so in an away game since Alan Smith in November 1998 (also at Anfield).
Van Dijk scored his 10th PL goal for Liverpool - more than any other centre back in the competition since his PL debut for the Reds in January 2018. Each of his last nine such goals have been headed.
Leeds are the first promoted side to score 3+ goals away at the reigning champions in the Premier League since Hull lost 3-4 vs Man Utd in November 2008.
Liverpool have now won each of the last 35 PL games in which Mo Salah has scored - he has overtaken Wayne Rooney's competition record of 34 consecutive wins when scoring from September 2008 to February 2011.