In the climax of Twilight Watch, how exactly does Anton outwit Kostya? For a moment, I thought that he, with all the power at his command, might have moved the spacestation itself. But that sounds improbable.
What did he do?
It's a fun coincidence that I finished re-reading this series two days ago. Awesome books, and I can't wait to get my hands on volumes 4 and 5, yet to be published around here...
I know the asker has obviously read the books up to this point, but for anyone that might want to read those books eventually (you should!), the answer cannot be given without spoiling more of the ending than what is contained in the question. Otherwise, please read on!
TL;DR : Others are magical parasites, and as such need humans to generate magic for them to use it. There are no humans in space (not enough, at least), so Anton realizes that if Kostya goes in orbit, he will be unable to use the Fuaran or to open a portal back home, essentially committing suicide. To prevent Kostya from learning this, he used all the accumulated power to shield his thoughts from him, then simply let him go. Kostya failed, then died a fiery death while re-entering the atmosphere a few days later.
It's quite simple, really. Earlier in the book, while hunting for the Fuaran, Anton learns from the witch Arina that all Others are no better than vampires, leeching magical energy from human beings. This is explained through the temperature analogy, where human beings generate a lot of heat (magical energy), but can't really store and use it. On the other end of the spectrum, Others are cold, possessing very little heat (magical energy), so they can absorb that of humans, then use it. Later on, Gesar goes on to explain that Others do generate some magical energy by themselves, but that they are, overall, absorbing a lot more than they are generating.
Kostya has had the Fuaran used on him while he was already a higher vampire, and thus became the (one of the?) most powerful Other in the world. Using the heat analogy, Anton describes Kostya as being an "absolute zero". As such, Kostya can wield great powers, but he's become unable to produce magical energy himself.
This is what Anton realizes: as an "absolute zero", Kostya needs humans around to wield any kind of magic. As there are no humans in space, Kostya will be unable to do anything magical once he gets there, whether it's using the Fuaran or opening a portal back home. Others are magical parasites, and by going where their food is non-existent is essentially committing suicide. For Kostya to actually go through with his plan, he must not be aware of that fact. But as the most powerful other in the world, he could easily read Anton's mind, which is why Anton uses his newfound Great Magician's powers, as well as all the magical energy provided by both Watches and the Inquisition, to shield his thoughts using a simple spell, but with enough power that Kostya couldn't pierce (detect?) it.
Kostya goes on with his plan, becomes unable to use magic, gets stuck in orbit. He can't die from lack of oxygen (vampires don't need to breathe), but he eventually burns entering the atmosphere a few days later.
As to why Kostya missed the space station, there is also an explanation. I don't exactly remember where in the series, but I distinctly remember one of the protagonists (Gesar, maybe? Or perhaps Anton, while describing the opening of a portal by Gesar) explaining that portals are a messy business. They require lots of energy to open, and even then, you can only open one to somewhere you're familiar with, or to a place where you've got a good grasp on its position. Kostya, while clearly well educated, is no physicist. His plan was to open a portal to the space station's altitude then wait for it to come by (they were sending a shuttle, so it was indeed coming by), then open a portal to the inside, since he'd now have a line of sight to his objective. A good plan, really, but for one little thing...