The Reds not only had a mountain to climb on the scoreboard, but were deprived of two of their most potent attacking weapons in Mohamed Salah and Roberto Firmino due to injury.
However, Origi and substitute Wijnaldum were the unlikely heroes as Barca surrendered a three-goal first-leg lead to exit the Champions League for the second straight season.
Despite the despondency of losing Salah and Firmino, Jurgen 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 in the Champions League on seven minutes on the rebound after Marc-Andre ter Stegen had denied Jordan Henderson's purposeful burst from midfield.
Liverpool have blown plenty of sides away in early bursts under Klopp, most notably hitting three inside the first half-hour at Anfield against Manchester City in last season's Champions League quarter-final.
Barca looked rattled as Sergi Roberto's short backpass nearly played Origi in.
However, the visitors soon started to pose a threat themselves in search of the away goal that would kill the tie.
Lionel Messi had turned the tie in Barcelona's favour late in the first leg with a brilliant free-kick and his first effort was tipped over by 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 an Andy Robertson drive and Alisson saved from Jordi Alba at the end of a pulsating first half.
Liverpool were seemingly dealt another injury blow as Robertson could not continue after half-time, but he made way for Wijnaldum with James Milner moving to left-back.
Wijnaldum sends Anfield wild
Alisson made another important save from Suarez before Wijnaldum sent Anfield wild twice inside two minutes.
Firstly, the Dutch midfielder was picked out by Trent Alexander-Arnold's low cross and drilled under Ter Stegen.
And from Liverpool's next attack, Shaqiri picked out Wijnaldum to head home at the Kop end.
Barca coach Ernesto Valverde tried to restore some order as Coutinho, who cost £142 million ($186 million) when moving between the clubs in January 2018, 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 were inexplicably caught cold from a quick Alexander-Arnold corner 11 minutes from time that picked out Origi completely unmarked to fire high past Ter Stegen.