Aspelin and Lindstedt defeated the Russian duo of Igor Kunitsyn and Dmitry Tursunov 6-4, 6-7 (6-8), 7-6 (8-6), 6-2, giving Sweden an insurmountable 3-0 lead in the opening round.
The doubles triumph built on Friday's singles wins for Sweden, which saw world No. 4 Robin Soderling defeat Igor Andreev 6-3, 6-3, 6-1, and Joachim Johansson best Teymuraz Gabashvili, 6-3, 7-6 (7-4), 6-4.
Russia was playing without top stars in Mikhail Youzhny and Nikolay Davydenko and fell in the Davis Cup first round for the first time since 2004.
Sweden now goes on to face the winner between Serbia and India in July's quarterfinals.