Barcelona defenders were like statues, failing to react to what Liverpool coach Jurgen Klopp called a "genius moment".
"We all know you need luck in this situation or a genius moment like Trent Alexander-Arnold," Klopp said.
"I saw the ball in the net and didn't know who had taken the corner, it was too quick for me. Oh my God — genius."
England great Gary Lineker tweeted: "One of the cleverest, cheekiest, most brilliant bits of football I've witnessed ... from the 20 year old."
Commentating for BT Sport, Lineker also said: "It is crazy to switch off from a set play like that."
Wijnaldum said the Liverpool players had the belief they could come back in the tie despite the first leg scoreline.
"Unbelievable. After the game in Spain, we were confident we could score four at home," he told BT Sport.
"Once again we showed that everything is possible in football. I was really angry at the manager that he put me on the bench but I had to do something to help the team when I came on.
"We believe it from the start. People from outside (the club) they thought it was not possible but we still managed to do this."
It loomed as an impossible task, recovering from a three-goal deficit after the opening leg but the miraculous 4-0 win at home now means Liverpool is headed for the Champions League final, and football supporters lost their minds.
Despite the despondency of losing Salah and Firmino, Klopp's men never lost faith and were accompanied by a typically raucous Anfield atmosphere on a European night.
Origi would almost certainly not have started had Salah and Firmino been fit. But the Belgian has made a habit of scoring important goals in Liverpool's challenge for a first Premier League title in 29 years and he had his first ever goal in the Champions League on seven minutes when he slotted home the rebound after Barcelona goalkeeper Marc-Andre ter Stegen had saved Jordan Henderson's shot.
Liverpool has blown plenty of sides away in early bursts under Klopp, most notably hitting three goals inside the first half-hour at Anfield against Manchester City in last season's Champions League quarter-final, and the trend continued today.
Barca looked rattled as Sergi Roberto's short backpass nearly gave Origi a path to goal. However, the visitors soon started to pose a threat themselves in search of the away goal that would kill off the tie and seal their progression through to the Champions League decider.
Lionel Messi had turned the tie in Barcelona's favour late in the first leg with a brilliant free-kick and his first effort today was tipped over the crossbar by Liverpool keeper Alisson Becker before the Brazilian denied international teammate Philippe Coutinho.
Another former Liverpool favourite Luis Suarez promised not to celebrate if he scored on his former stomping ground, but there was no love lost for the Uruguayan among the home faithful as he was showered with abuse after trying to buy cheap free-kicks.
Ter Stegen nervously parried away an Andy Robertson drive and Alisson saved Jordi Alba's effort at the end of a pulsating first half.
Liverpool was seemingly dealt another injury blow as Robertson could not continue after half-time, and he made way for Wijnaldum with James Milner moving to left-back.
Alisson made another important save from Suarez before Wijnaldum sent Anfield wild twice inside two minutes. Firstly, the Dutch midfielder was picked out by Alexander-Arnold's low cross and drilled the ball under Ter Stegen and into the back of the net.
And from Liverpool's next attack, Shaqiri picked out Wijnaldum to head home the team's third goal.
Barca coach Ernesto Valverde tried to restore some order as Coutinho was replaced for the second time in the tie by Nelson Semedo to allow the visitors to switch to a four-man midfield.
The change briefly had an impact, but Barca was inexplicably caught cold from a quick Alexander-Arnold corner 11 minutes before full-time that picked out an unmarked Origi, who blasted the ball past Ter Stegen to secure the dramatic win.
Liverpool players were ecstatic after the win as they took to social media to reflect on the astonishing performance, which will see them play either Tottenham or Ajax in the final in Madrid on June 1.
