Both teams needed a win to have any chance of topping the group in the 725,000 US dollar event after losing their opening ties.
But the weakened Russian combination of Yuri Schukin and Svetlana Kuznetsova showed greater passion than the Swedish team of Thomas Johansson and Sofia Arvidsson, although they had to rely on a tight mixed doubles to clinch the tie.
The result meant that all eight ties in the tournament, being played at the Burswood Dome, have so far finished 2-1.
Earlier in the day, second seeds Argentina, represented by Gisela Dulko and Gaston Gaudio set up an equally-intriguing race to top Group B after they beat the German pair of Anna-Lena Grönefeld and Nicolas Kiefer.
Only hosts Australia are now out of contention in that group with the Netherlands, Argentina and Germany all still in with a chance to reach Friday’s final.
Russia had come close to claiming a 2-0 lead in their tie when the unheralded Schukin, ranked 299 in the world, took Johansson, a former Australian Open champion, to the wire before losing 7-6 (9/7), 7-6 (7/4).
Schukin was only drafted into the tournament at the last minute following the withdrawal of first choice Marat Safin and second replacement Teimuraz Gabashvili.
The 26-year-old was rushed to Perth from Moscow on New Year’s Eve as organisers searched frantically for an available replacement.
In the end it was only Johansson’s serve that saved him in two tie-breaks after he landed 19 aces to one but clocked up 40 unforced errors.
The Swede said Schukin had used the bounce of the hardcourt surface to throw his game out.
“Today I was struggling with the high ones. I think he played a good tactic against me but luckily I was serving well and I just tried to hang in there,” Johansson said.
“If we had gone three sets, he looks pretty strong so I was a little bit worried there so luckily I could finish it in two.”
Former US Open champion Kuzsnetsova had earlier claimed the women’s singles with a 7-6 (7/3), 6-4 win over Arvidsson.
In an extraordinary match which included 29 break points, the pair exchanged service 13 times with the first set lasting 57 minutes.
“It’s women’s tennis — we do lose lots of serves,” Kuznetsova laughed.
“The match was not very consistent. I did so many unforced errors, I had so many chances and I didn’t use them.
“Today I didn’t move my legs behind the ball as well as I have to put so many forehands in and that’s why I did so many unforced errors.”
Kuznetsova also revealed she would team with France’s Amelie Mauresmo in the mixed doubles at the Australian Open later this month after her regular partner Alicia Molik of Australia was forced out with illness.
Earlier in the day, former world number four Kiefer signalled his intentions for the Australian Open when he cruised past Argentina’s Gaudio 6-3, 6-3, but the German’s efforts weren’t enough to carry his team to victory.
Instead Argentina, the second seeds for the event, kept their hopes alive with a 2-1 win in Group B, inspired by solid performances from Dulko in both the women’s singles and the deciding mixed doubles.
Dulko set her team on a course for victory when she took just 57 minutes to trounce Grönefeld 6-1, 6-0.
She then teamed with Gaudio in the mixed doubles, where the pair clawed back from the brink of losing the first set, to take the rubber 7-5, 6-0.
Unseeded Germany were favourites with local bookmakers to win the tournament and Kiefer’s effort to level the tie showed why.
On Thursday Australia play Argentina, Germany meet the Netherlands, Russia take on Serbia and Montenegro and the United States are pitted against Sweden.