Eight goals in either half saw Team GB come up short against the Beijing 2008 silver medallists, who had Lyudmila Postnova in superb scoring form.
But a strong performance from goalkeeper Sarah Hargreaves and a never-say-die spirit from Jesper Holmris' side meant Russia needed to work hard for the win.
Great Britain made a solid start, trading goals with Russia in the first five minutes as both sides went toe-to-toe.
But they needed goalkeeper Hargreaves on top form as the Russians looked threatening on the fast break as Great Britain were sloppy with possession.
Great Britain were making chances to score, but when there was turnover on the ball, the British team were wasteful, and were hit hard on the break, trailing 9-4 at the halfway point of first half.
Holmris was asking his defence to concentrate on firming up the middle as Russia threatened to open up an unassailable lead.
However, each time the hosts looked to be struggling to contain their opponents despite goals from Lyn Bil and Zoe Van Der Weel.
But Team GB were still poor with their passing - the usually reliable Lynn McCafferty the main culprit when she had two stray passes turned over and finished in style by Russia danger woman Emiliya Turey for a 17-8 half-time lead.
Russia stretched their lead to 12 after the half as Great Britain tried to keep up with the four-time world champions.
Hargreaves was in fantastic form as she made 11 saves to keep Team GB's morale high and McCafferty picked up her own game and got her first goal of the night.
Russia picked up their tempo and were looking likely to score each time they attacked, as Great Britain continuously left gaps in the half back position and Russians drove through to score.
Great Britain, who were expected to lose heavily, were working hard to keep the score down to aid goal difference, and with five minutes left, the score was 33-15.
Russia knew they were in a game, despite the comfortable lead, and were starting to lose their discipline, picking up two-minute suspensions, including Natalia Shipilova, as the clock counted down.
Reigning champions Norway came back from their shock 24-23 defeat to France in their opening match with a 24-21 win over neighbours Sweden in the last evening game.
Speed was more prominent in South Korea's narrow 25-24 win against three-times champions Denmark, the Beijing bronze medallists profiting from a series of fast breaks to move nearer to quarter-final qualification.
South Korea top Group B with four points, as do Russia in Group A where Croatia recorded their first win by beating Angola 28-23 to leave the Africans winless and second-bottom, above Britain.
Brazil scraped a fast-paced game against debutants Montenegro 27-25 to lie second in Group A.
French President Francois Hollande watched on as his nation staged a last-gasp comeback to draw with Spain 18-18, Allison Pineau firing in a low slinger with six seconds on the clock.
Hollande, who had been at the judo earlier and was heading to watch France's swimmers in action, posed with several fans rejoicing after the late-show by his nation's side.
The atmosphere did not abate for the all-Scandinavian tussle between world, Olympic and European champions Norway and Sweden, who fought back to within two goals with a minute remaining but lost to sit bottom of Group B without a win.