Marc Wilmots' side looked set to suffer frustration at the Maracana on Sunday after looking short of ideas against Fabio Capello's well-organised team.
However, teenage striker Origi came off the bench to grab an 88th-minute winner - his first international goal - and secure progression from Group H with a game to spare.
Two substitutes, Marouane Fellaini and Dries Mertens, had combined to help Belgium come from behind to beat Algeria in their first match, and another change paid dividends for Wilmots on this occasion, leaving Russia stunned.
Prior to Origi's strike, Belgium had hit the post through Kevin Mirallas, while Russia striker Aleksandr Kokorin spurned the best chance of the first half when heading wide from an unmarked position.
Russia, who were held by South Korea in their opening game, will now require assistance from elsewhere if they are to join Belgium in the knockout stages.
Fellaini and Mertens were rewarded for their goalscoring exploits against Algeria with places in the Belgium starting line-up, at the expense of Nacer Chadli and Mousa Dembele, while skipper Vincent Kompany was passed fit and Thomas Vermaelen came in for Jan Vertonghen.
Alexei Kozlov and Maxim Kanunnikov came into the Russia side, with Andrey Yeshchenko and Yuri Zhirkov dropping to the bench.
Belgium made a positive start, but it was Thibaut Courtois who made the first save of the game when he got down well to keep out Viktor Fayzulin's left-footed strike from just outside the penalty area 11 minutes in.
Mertens was proving to be a real handful for the Russia defence and the Napoli winger fired wide with his right foot after an incisive run.
Russia could have had a penalty when Kanunnikov went down under a challenge from Toby Alderweireld in the penalty area, but referee Felix Brych waved play on.
Vermaelen suffered an injury in the warm-up and was subsequently forced to come off shortly after the half-hour mark, so Vertonghen entered the fray.
Mertens remained Belgium's biggest threat and Russia goalkeeper Igor Akinfeev had to be alert to palm the winger's cross away after he cut in from the right at full tilt.
Yet Russia should have been in front two minutes before the break, when an unmarked Kokorin could only head Denis Glushakov's inviting cross wide of the target.
Wilmots replaced the ineffective Romelu Lukaku with Origi 10 minutes into the second half in an attempt to gain some impetus.
Both sides still looked devoid of ideas, though, with Belgium sitting deep and inviting Russia to break them down but Capello's side lacking quality in the final third.
Russia sensed the opportunity to snatch all three points, but they failed to create clear-cut opportunities in the second half and Glushakov was off target when he tried his luck from outside the penalty area.
Substitute Yeshchenko came close 10 minutes from time when he shot wide of the far post, while Mirallas then rattled the post with a free-kick.
Russia were then stunned two minutes from time as Eden Hazard embarked on a fine run to the byline and cut the ball back for Origi, who was on hand to fire home and see Belgium through.
