At the other end of the table, Cardiff were relegated after their 3-2 defeat against Crystal Palace.
Liverpool's thrilling title battle with Manchester City is now guaranteed to go down to the final day of the season as Jurgen Klopp's men moved two points ahead once more at the top.
City have a game in hand, at home to Leicester on Monday, but Liverpool refuse to give up in their pursuit of a first title for 29 years.
"If we are champions then we are champions, you can't feel pressure when you do your best," said Klopp.
"94 points is incredible. Today was a battle of will but it was a victory of passion, heart and absolute desire -- absolutely brilliant."
Virgil van Dijk headed the visitors into an early lead at St. James' Park, but Liverpool were fortunate when Newcastle levelled through Christian Atsu.
Liverpool right-back Trent Alexander-Arnold had handled Salomon Rondon's effort on the goal line and could have conceded a penalty and been sent-off after just 20 minutes had Atsu not put home the rebound.
Alexander-Arnold was the creator as Klopp's men quickly retook the lead through Salah.
However, Rondon levelled once more for Newcastle early in the second half.
Salah then had to be stretchered off with a head injury after clashing with Newcastle goalkeeper Martin Dubravka, which will make him a doubt for Tuesday's Champions League semi-final, second leg against Barcelona.
Yet, despite also missing Roberto Firmino through injury, Liverpool found a response four minutes from time when Origi flicked home Xherdan Shaqiri's free-kick.
"You feel the emotion. It's a very special season for everyone," said Origi. "But as a player you have to channel that feeling into the performance and in the end it worked out."
- Spurs slip up again -
Tottenham also have a 1-0 Champions League semi-final deficit to overturn against Ajax on Wednesday, but still have work to do to qualify for the competition next season after a sixth straight away league defeat.
Son Heung-min and Juan Foyth were sent-off either side of half-time.
Mauricio Pochettino's side looked like they would hold on for a point as the match entered stoppage-time, but Bournemouth defender Nathan Ake ended third-placed Tottenham's stubborn resistance to delay their attempt to guarantee a place in the top four.
Fourth-placed Chelsea will now go above Spurs if they defeat Watford and Arsenal, currently fifth, will move to within one point of their north London rivals if they beat Brighton on Sunday.
"We need to move on. We have ahead two finals," said Pochettino.
"It is in our hands. If it does not happen we will be proud because nobody expected Tottenham to be in the position they are today."
Cardiff needed a win to have a realistic chance of beating the drop on the last day of the season, but they were out-classed by Palace in south Wales.
Wilfried Zaha put Palace ahead in the 28th minute before Martin Kelly's own goal three minutes later gave Cardiff hope.
Michy Batshuayi restored Palace's lead in the 40th minute and Andros Townsend made it three after 70 minutes, with Bobby Reid's 90th minute goal little consolation for Cardiff.
"They've tried hard. We've shown limitations today and that's why we are where we are," said Cardiff boss Neil Warnock.
In their first season back in the top-flight, Wolves moved a step closer to sealing an impressive seventh place finish as Leander Dendoncker clinched a 1-0 win over relegated Fulham.
If Manchester City win the FA Cup final against Watford later on May 18, the team which finishes seventh will go into the Europa League qualifying rounds next season.
Marko Arnautovic ended his 11-game goal drought with a brace in West Ham's 3-0 win against Southampton at the London Stadium.
Salah was stretchered off 20 minutes from time making him a doubt for Tuesday's Champions League semi-final, second leg against Barcelona, while Klopp confirmed Roberto Firmino will definitely miss the visit of the Spanish champions to Anfield.
"We'll have to see. He (Salah) took a blow to the head. He watched the game in the locker room, he was OK, but we have to do more tests," Klopp told Sky Sports.
Overturning a 3-0 first leg deficit against Barca now looks an even more monumental task, although Liverpool stay in the hunt for the Premier League title.
However, rivals Manchester City have two games remaining to Liverpool's one.
In a recurring theme of a thrilling title race, Liverpool dug deep late on to continue asking questions of the champions by moving two points ahead of City once more.
"I accepted long ago we do everything (we can)," said Klopp, whose side have lost only once in the league this season.
"Whether we will be champions or not is destiny because we cannot do more.
"Even in the draws we tried everything to win the games. The boys showed in each second they really want to win it."
Faced with a difficult balancing act to strike, Klopp made four changes to the side beaten by Barcelona in midweek.
Trent Alexander-Arnold was one of those recalled and the England right-back was to have an eventful evening at both ends.
Alexander-Arnold's corner found Van Dijk completely unmarked to open the scoring as Rondon slipped and the PFA's Player of the Year powered home his fifth goal of the season.
Newcastle had barely ventured over the halfway line in the first 20 minutes, but levelled with their first serious attack.
Matt Ritchie's driven cross was turned goalwards by Rondon, whose shot was saved on the line by the arm of Alexander-Arnold.
A penalty and a red card would likely have followed for the Liverpool defender had Atsu not put home the rebound.
All of a sudden Newcastle looked the more dangerous side as Ayoze Perez turned Van Dijk before smashing off the crossbar.
However, an enthralling first 28 minutes took another twist when Alexander-Arnold made the most of his reprieve to still be on the field with his second assist of the night.
His cross found Salah inside the area, but the Egyptian still had plenty to do as he cushioned a finish into the far corner on his weaker right foot to move two in front of teammate Sadio Mane and Sergio Aguero in the race for the Golden Boot.
Newcastle boss Rafael Benitez could have been taking charge of the Magpies for the last time at home as the Spaniard's contract runs out at the end of the season.
But his side did not go down without a fight as Rondon's sweet strike levelled once more early in the second half.
"We will have conversations in the next couple of weeks. It is so simple, you can see the potential," said Benitez, whose four seasons at the club have been marred by a frosty relationship with owner Mike Ashley.
"I am really proud and pleased because we stayed up but I would like to do something more."
Salah was caught on the head by Martin Dubravka as Newcastle's Slovakian goalkeeper raced from his goal to punch the ball to safety.
He was stretchered off, his hands over his face to applause from both sets of supporters.
"He got the hip of the goalie on his head," added Klopp. "When we came in he was sitting in the dressing room and watched the game. He was then fine but we have to wait."
Without two thirds of their prolific frontline, Liverpool would have been forgiven for thinking their chase of City was up.
But, not for the first time this season, Origi, who scored a 96th minute winner against Everton in the Merseyside derby in December, came off the bench to score a vital late goal as he got his head to Xherdan Shaqiri's free-kick.