Jordan were hoping to win their first-ever World Cup match after they took the lead in the 36th minute on Monday.
Mousa al-Tamari couldn't collect a cross but the ball found Nizar al-Rashdan, who smashed it into the net.
But Algeria hit back in the second half and equalised in the 69th as Nadhir Benbouali rose to meet Riyad Mahrez's corner and head it into the goal.
They completed the turnaround in the 82nd, again from a corner. The ball was loose in the ball after a header but Amine Gouri recovered it and tapped it in for the winner.
"It was a very hard game. They were leading 1-0 but we had the upper-hand the whole game, that was my feeling," midfielder Ibrahim Maza said.
"We spoke during halftime that we had to do even more but be patient still. Then we scored two nice goals and we won the game. We're very happy."
Argentina top Group J with six points after they defeated Austria 2-0 earlier with two goals for Lionel Messi, who's now the all-time World Cup top scorer.
Algeria are third but tied on three points with second-placed Austria, whom they face in the final group-stage match on Saturday.
Jordan will farewell the tournament after their clash against Argentina.
"The three points help us for the next game, it will give us confidence," Maza said.
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