Coach Vladimir Petkovic's side had been outclassed 3-0 by the defending champions but showed resilience and determination to beat Jordan, who were riding a wave of euphoria from their first-ever World Cup appearance.
In the all-Arab clash at San Francisco Bay Area Stadium, Algeria, who used 14 players from clubs across seven European countries, combined precise passing with deft touches and adventurous runs in a relentless push to get their World Cup back on track.
Petkovic's decision to start with captain Riyad Mahrez proved decisive in the 2-1 win. The former Manchester City forward was energetic, menacing and a central figure in their rally, providing the corner for Nadhir Benbouali's headed equaliser.
Amine Gouiri scored the winner eight minutes from time when he poked home a loose ball, triggering jubilation on the pitch and in the stands, and condemning Jordan to an early World Cup exit.
"We had the mental strength to come back, and I think we're continuing to improve. This victory, earned with character and determination, will do us the world of good," Gouiri said.
"It could be a turning point. A win is always good, especially for confidence given the way the match unfolded. We're very happy, but we know nothing is done yet. We've taken an important step."
Algeria had the majority of possession and 16 attempts on goal as they battled to break down a compact and organised Jordanian defence.
Stifled on the flanks, they were creative in the middle, with Marseille's Gouiri linking up with Bayer Leverkusen's Ibrahim Maza, and Hicham Boudaoui sending two perfectly weighted passes from deep inside his half into the path of Mahrez.
Algeria, who last appeared at the 2014 World Cup, are hoping the expanded 48-team tournament will make it easier for them to reach the knockout rounds and offer them the chance to write a new story that goes beyond their famous 1982 upset of West Germany.
They face Austria in their final Group J game on Saturday.
