Seeking to avenge their 2-0 defeat in Stockholm in 2018 that saw the Swedes promoted to UEFA Nations League Group A ahead of them, the Russians piled the pressure on early, and Anton Miranchuk came close to breaking the deadlock in the 17th minute with a shot that thumped off the crossbar.
That miss was to prove costly four minutes later when Sweden were awarded a free kick in the centre of the pitch, and Isak ghosted into the space between defender Ilya Kutepov and goalkeeper Soslan Dzhanaev to head home.
With Nations League games against Croatia and Portugal next week, Sweden coach Janne Andersson fielded an experimental line-up, giving central defender Carl Starfelt, who plays for Russian club Rubin Kaxan, his first cap.
Andersson was rewarded in the second half when right back Johansson, returning to the squad for the first time in six years, struck a deflected effort that wrong-footed the keeper in the 73rd minute to make it 2-0.
Russia's best opportunities came from the left flank, and Aleksandr Sobolev, making his senior international debut, muscled his way through the Swedish defence to head home Denis Cheryshev's corner in stoppage time for a consolation goal.