Originally Posted by SQFreak

Well, not really. You can take a bus to Domodedovskaya metro or the Aero Express to Paveletsky vokzal, which is attached to Paveletskaya metro.
Either way, take a green (2) line train to Teatralnaya. It may be fastest to transfer underground to Okhotny Ryad, because Teatralnaya is a few blocks away while Okhotny Ryad is directly across from Red Square, and you won't have to traverse any busy streets.
I think, if the train times work for you, the Aero Express to Paveletsky might be faster than a taxi, given what traffic can be. That should be about 1.25 hours door to door.