Liverpool were reeled in three times before they finally got the decisive goal four minutes from the end.
It was via a penalty from Mo Salah who was completing his hat-trick.
The Egyptian was superb all through this match, even if the first of his three goals also came from the spot.
While many of his team-mates seemed lethargic at times, Salah was full of life, laying on chances and buzzing around the Leeds penalty area.
For all of this game, Leeds lived up to the expectation of them being the Premier League's entertainers this season.
Their defence rocked at times, but club captain and centre-half Liam Cooper was missing after being injured on Scotland duty.
He'll add a bit to their defensive resources when he returns.
And certainly playing like this in every match will see Leeds sitting at halfway in the Premier League table next May.
Mind you, defending like this will see Liverpool handing over the trophy they laboured to win last season.
Perhaps the game being billed as the Premier League champions against the Championship winners lulled Liverpool into thinking this would be easier than it proved to be.
For all that Liverpool were superb in attack, they were seriously sloppy in defence.
It was the game Leeds supporters had waited for since May 2004, when they were last a Premier League club.
Frankly it didn't disappoint!
They finally got to see their team play in the top flight, even if they didn't see any points at the end of it all.
Three of those seasons were even spent in League One as a proud club tumbled down English football's tree.
There were possibly easier openers for this season than the one the fixture computer game them - and a shocking start only added to their troubles.
Not even three minutes had passed when Leeds' new German international centre-half Robin Koch had his arm away from his body when a Mo Salah shot deflected off his knee up onto his arm.
Under the new penalty rules in force this season, the spot-kick was given and Salah, newly-shorn for the start of the season, smashed the ball to the net.
Yet Leeds were not daunted and surged forward towards the Kop.
Helder Costa had the ball in the Liverpool net, before being called back for offside.
But when Jack Harrison put it there after 12 minutes, this one counted.
New England international Kalvin Phillips played a great ball to Harrison, who took the pass on his instep and skipped inside Trent Alexander-Arnold to score.
Virgil van Dijk soon put Liverpool back in front with a thumping header from a corner.
However this was no ordinary match and a crazy game took another turn on the half-hour when Patrick Bamford levelled for Leeds.
Yet it was how the goal came about that was intruiging - a bad mistake by van Dijk.
They are not words often written, but the Dutchman was at fault as he casually poked away a long ball.
But it fell to Bamford who tucked the loose ball beyond Alisson.
Still the goals wouldn't stop raining in and Liverpool took the lead for a third time when Salah thrashed home a great drive after three Leeds players had gone to cover van Dijk at a free-kick.
It was lunatic stuff, thrilling in fact for the millions watching at home on the TV.
But two coaches like Jurgen Klopp and Marcelo Bielsa, who like their teams to get the basics right, could not have been happy with what was unfolding in front of their eyes.
This was comic cuts defending with neither side able to simply clear their lines when the need arose.
It couldn't continue like that and it didn't.
The second half was still entertaining, still with goal chances at either end, but for a while the goals dried up.
The lull pointed us towards Liverpool coasting to a first day win, but Leeds simply would not settle for an honourable defeat.
And in the 66th minute, Leeds' Polish international midfielder tied it all up for the third time.
Klich has been one of the mainstays of Bielsa's time at Elland Road, being picked for every Championship match he was available for.
And he repaid that loyalty from the Argentine manager, cracking home a fine finish that would have silenced the home crowd - if there was one!
It seemed to set Leeds up for an unlikely point, but the top-flight champions at last began to find their mojo and they turned the screw.
Both Salah and Firmino missed good chances to put Liverpool ahead, before Salah had the last word of a cracking 90 minutes after Leeds' sub Rodrigo stuck out a lazy leg and brought down Firmino.
"It was a very tough game for us," Salah admitted afterwards.
"They press very high up the pitch and so that led to a game of real intensity.
"Normally we don't concede three goals in a game so that is something to work on, but this was a tough game for us."
For Liverpool, it was the first three points on the march to a second title, but they will have to improve big time on this effort.
Teams are going to be gunning for them now.
Leeds can take their strong performance out of the match as encouragement for the future.
But Bielsa will be telling his players that for all the good football they produced, they went back to Yorkshire last night with no points.
And in the sometimes cruel world of football, that is what he wil focus on in the coming days.