Honoured before kick-off at the Parken Stadium in the Danish capital, Sorensen was beaten after only four minutes as Shirokov fired home low to the keeper's right.
Despite some tidy touches from Christian Eriksen and William Kvist in Denmark's midfield, Arshavin doubled Russia's lead just before half-time when he drifted in from the right before lashing a powerful drive past Sorensen.
"It was a good win against a team that is difficult to beat. The first 20 minutes we controlled the game and created chances without giving any chances away," Russian coach Dick Advocaat told reporters.
Forward Arshavin, who returned to Zenit St Petersburg on loan earlier this month after an unhappy spell at Arsenal, was instrumental in the victory.
"I was happy for the team and happy for Andrei, after a very difficult period at Arsenal. Now you can see what kind of a player he is," added Advocaat.
The closest Denmark came to a goal was a free-kick by Eriksen, but the attacking midfielder's strike was punched away by Russia keeper Vladimir Gabulov.
"The positive is that we created chances. The negative is that we didn't score," said Denmark coach Morten Olsen.
