Spain took control in the first half with a ninth-minute header from Jordi Alba and a fortuitous penalty for handball which defender Sergio Ramos coolly converted in the 35th.
Russia, who drew with Iran and lost to Argentina in their previous two friendlies as they build up to the 2018 finals, got back into the game with a brilliantly-worked team move finished off by striker Fedor Smolov four minutes before halftime.
Midfielder Alexei Miranchuk then ghosted in at the near post to equalise five minutes into the second half, although Spain quickly reestablished their lead three minutes later thanks to another penalty scored by captain Ramos.
However, Russia hit back again with another lightning move, recovering the ball following a Spain throw-in and working the ball to Krasnodar striker Smolov, top scorer in the Russian Premier League for the last two seasons, who unleashed a deadly strike past helpless keeper David de Gea in the 70th.
It was the first time Spain had conceded more than two goals in 90 minutes since they were hammered 5-1 by the Netherlands in the opening game of the 2014 World Cup.
They could even have suffered a first defeat under Lopetegui when Smolov cut inside the area but De Gea kept out his shot.
In the last minute of normal time Spain forward Rodrigo Moreno tried to reach a loose ball and collided with Russia keeper Andrey Lunev, who had to be carried off on a stretcher.
(Reporting by Richard Martin; Editing by Ken Ferris)
