The away side came from behind three times and looked set to be earning a precious point until Salah converted an 89th-minute penalty after Leeds’ club record signing Rodrigo fouled Fabinho to concede the spot kick.
Promoted as champion from the English second flight last season, Leeds put on a command performance to push Liverpool all the way in a match that would have graced a packed stadium rather than a scattering of squad players and officials.
Egyptian star Salah, who looked sharp throughout, proved the difference, putting his side in front with his first successful conversion from the penalty spot after four minutes and completing the first half scoring with a laser-like finish to edge his side 3-2 ahead in an extraordinary five-goal first half.
Leeds, playing with the high-tempo pressing style so typical of Bielsa’s sides, leveled at 3-3 on Mateusz Klich’s 66th minute goal, which he started and finished. But Leeds could not hold out under intense pressure from Jurgen Klopp’s men.
Returning to the top-flight after 16 long years, Leeds could scarcely have made a poorer start as new signing Robin Koch conceded a penalty as Salah’s shot deflected from his knee onto his outstretched arm.
Leeds protested to referee Michael Oliver, but his decision was confirmed by the video assistant referee and Salah blasted the ball home down the middle.
But any thoughts of an easy home victory were quickly put to bed as new England international Kalvin Phillips found Jack Harrison with a raking long pass and the on-loan Manchester City man did superbly to cut inside and beat Alisson Becker with a powerful low shot on 12 minutes.
Liverpool went ahead again eight minutes later as Virgil Van Dijk powered home a header from an Andy Robertson corner but the Dutch defender was at fault soon afterward for the second Leeds equalizer.
He miscued a clearance and Patrick Bamford was on hand to score neatly to make it 2-2.
Both sides were showing defensive frailty and it was another indifferent clearance from a free kick that afforded Salah the opportunity for his second goal, controlling quickly before powering his shot into the top left of the Leeds net.
The second half was a calmer affair, with Leeds matching Liverpool for possession and deservedly leveling through Klich’s fine strike until striker Rodrigo, making his debut, mistimed his challenge to concede a needless penalty that Salah was never going to miss.
Salah acknowledged the part the opponent had played in a pulsating start to the new season.
“Leeds are a tough team. They had a great game and reacted really well,” he told Sky Sports.
“I’m happy about the result and we have to keep on improving. It’s important for me to stay focused. We had a good game.”
Klopp summed up the thoughts of many after a memorable clash.
“What a game. Football as it’s best. What a spectacle,” the Red boss said.
Lacazette at the double
The opening goal of the Premier League campaign was scored by Alexandre Lacazette as he helped Arsenal to a thumping 3-0 win over promoted Fulham in the early kick off.
Fulham started brightly but that initial good work was undone by sloppy defensive work as Arsenal’s new signing Willian set up the Frenchman in a goalmouth scramble for his ninth-minute strike.
It is the second time Lacazette has scored the first goal of the Premier League season, achieving the feat in 2017-18 against Leicester City.
Fulham fought hard to retrieve the situation but the Cottagers fell further behind at the start of the second half as Arsenal’s new signing Gabriel Magalhaes scored after a corner, the ball finding the net off the top of his shoulder.
The icing on the cake for Mikel Arteta’s FA Cup winners came later in the second half as a sublime team move saw Pierre-Emerick Aubameyang get off the mark for the season to make it 3-0 with his 11th goal in 11 games for the Gunners.
In the afternoon match, Wilfried Zaha scored the only goal as Crystal Palace beat Southampton 1-0 at Selhurst Park.
Zaha, linked with a move away from Palace, volleyed home in the 13th minute on an assist by Andros Townsend.
Southampton pressed hard for an equalizer with last season’s top scorer Danny Ings denied by a fine late save from home keeper Vicente Guaita.