US Eagles fly half and man-of-the-match Nese Malifa said: "We knew Russia were going to come out hard and that we had to take the fight to them. Hats off to the boys - it was a big day at the office."
The teams will meet in New Plymouth, New Zealand on September 15 and Russian boss Kingsley Jones admitted: "If we could have kept hold of the ball more we could have won. USA were smarter than us at the breakdown. We are taking two steps forward and one step back but we need to take the positives out of this tournament."
Yury Kushnarev and Malifa traded early penalties in an even first 20 minutes before the USA No 10 put a second chance wide.
The Eagles made several breaks and they eventually got through after Andrew Suniula brushed off five tacklers before being hauled down short of the line. The ball was recycled and Malifa sent Paul Emerick over.
Russia hit back to level the scores at 8-8 with a try from Vladimir Ostroushko after taking Kushnarev's miss pass after a solid scrum platform put the Eagles under pressure.
And the Bears almost scored the try from the end of Sixways when they counter attacked from in front of their own posts and, 80 metres later, only a knock-on prevented the score.
The Russians, intent on keeping the ball in hand, spurned a penalty chance to go for touch but their endeavour was not matched by their ability to win the subsequent line-out and the chance was lost.
Kushnarev and Malifa added another penalty apiece before Russia grabbed their second try when Igo Klyuchnikov made the break, Ostroushko jinked his way closer down the wing and Alexander Voytov trundled in from Alexander Sahkirov's pass.
Malifa kept the Eagles in touch when he created a try for Suniula, who checked and sped to the line and it was all USA as Clever intercepted the ball in a flat Russian back line move to race 70 metres and score to put them 25-18 up.
But the Russians weren't out of it and Vasily Artemyev stepped inside and burrowed over for Kushnarev to convert and level the scores.
USA had a chance from halfway to edge ahead but Clever opted for the lineout which crumbled but they kept up the pressure and Blaine Scully insitigated the counter attack for Emerick and Suniula to combine and send Enosa over.
USA: B Scully; C Hawley (T Enosa 59), P Emerick, A Suniula, K Swiryn; N Malifa, M Petri (T Usasz 62); M Moeakiola (E Fry 68), P Thiel, S Pittman, J Van der Giessen, S Lavalla, I Basauri (N Johnson 62), T Clever (capt), L Stanfill (P Danahy 78). Reps (not used): C Biller, R Suniula.
Scorers: Tries: Emerick, Suniula, Clever, Enosa; Pens: Malifa (2); Cons: Malifa (3).
Russia:I Klyuchnikov; V Artemyev, M Babaev, A Makovetsky, V Ostroushko; Y Kushnarev, A Shakirov; S Popov, V Korshunov (capt), I Prishchepenko, A Voytov, D Antonov, A Temnov, A Garbuzov (V Gresev 36-40, A Panasenko 62), V Grachev (Gresev 50). Reps (not used): V Tsnobiladze, A Chernyshev, A Bykanov, A Ryabov, I Galinovsky.
Scorers: Tries: Ostroushko, Voytov, Artemyev; Pens: Kushnarev (2); Cons: Kushnarev (2).
Referee: D Pearson (RFU)