Morten Olsen's men struggled to contain the visitors for large parts of the match, and paid the price for their inept defensive performance and inefficiency in front of goal
Dick Advocaat's men hit the hosts with a first-half double salvo, courtesy of Roman Shirokov and Andrey Arshavin, which proved enough to secure victory.
The game got off to the worst possible start for the Danish as in the fourth minute some hesitant defending from Morten Olsen's men resulted in the opener.
Arshavin picked out Shirokov just outside of the box, and the former CSKA Moscow man easily beat Thomas Sorensen with a low shot in the left corner, with defender Andreas Bjelland a mere spectator.
Denmark responded almost immediately through Simon Poulsen, who saw a shot from inside the box saved by goalkeeper Vladimir Gabulov after a great run on the left flank. Olsen's team continued to press, but Russia had little trouble containing the hosts' toothless attacks.
Hesitancy from Dick Advocaat's men nearly gifted Denmark the equaliser, however, in the 22nd minute. Dennis Rommedahl created a clear-cut chance for Nicklas Bendtner, but the Sunderland striker missed the target from just eight yards out.
The hosts let another great opportunity pass by just before the half-hour mark as Simon Kjaer sent a header over the bar under pressure from Sergei Ignashevich, whose challenge might have resulted in a penalty.
Shortly after, however, Russia almost doubled their lead as an inept backheel clearance by Simon Poulsen gifted the ball to the onrushing Igor Denisov, who struck the ball first time, but saw his finish claimed by Sorensen.
Arshavin was not as forgiving, however. Just before half-time the Zenit man was picked out on the edge of the box, and took a few steps before firing a powerful shot past the goalkeeper.
Denmark introduced Tobias Mikkelsen in place of Michael Krohn-Delhi at the beginning of the second period, and the substitute nearly made an instant impact.
In the 49th minute he was released through on goal, and managed to round Gabulov on the left side of the box, but his follow-up finish was cleared at the near post. Mikkelsen had another chance shortly after, but was once again denied by the goalkeeper.
On the hour mark, Bendtner once again paid the price for his hesitancy in front of goal as he saw a shot blocked by Ignashevich after he was picked out by AZ full-back Poulsen from the left flank.
Denmark pushed hard for a consolation strike, but the closest they went to clawing one back was in the 82nd minute when Mikkelsen was released in a one-on-one with Gabulov, but was flagged for offside just before he could pull the trigger.
In the end Russia were good value for their win, and give Denmark food for though as Euro 2012 edges ever closer.