I think I just got back from my closest game in a long time:
I recently moved up to Prince, and I can win about 75% of the time. In my last game, there were four civs left by 1900, and we each had a continent or island to ourself. Because land is power, the two continents were miles ahead of the two islands. The two islands were non-factors, but Zara Yaqob of Maya was giving me (Darius of Rome) quite a run for my money. We had a centuries long cold war, where I always lagged just behind him in the power graph-- I couldn't hope to attack him successfully, but I was strong enough that he had no interest in attacking me.
I was frantically playing catch-up. and I considered the options-- take over the two islands and go for some sort of domination win, or hole up inside my own borders and go for a space race/cultural?
I hadn't laid the groundwork for cultural, and I was afraid that getting bogged down in a third world country would just let Maya get more ahead. So, I went for the space race. I bee-lined all spaceship techs, and left off anything that wasn't needed (including, amusingly enough, flight). I used two great engineers to ensure that I would get the space elevator, went straight to superconductors for labs, and then devoted all my production to spaceship parts and counter-espionage.
When I was still researching genetics, Maya came within 15 turns of winning a cultural victory. I lucked out, though, and he neglected to heavily defend one of his key cities that was coastal. I sent three transports full of modern armor on a suicide mission (I contemplated taking destroyers to bombard city defenses, but my navy was scant, and I couldn't lose them on a doomed suicide mission). Sneaking through a third civ's territory, I DOWed and amphibiously assaulted Chitchen Itza on the same turn, burnt it to the ground, then let my units nobly endure counter-assaults until they got blowed up.
His transports were deflected with relative ease (thanks guided missiles, submarines), but he had a third city that was rapidly moving up the culture ranks. I quit making military units, knowing I'd have to rely on my reserves. I still needed genetics to be able to build the last part, so every city converted all its hammers to research. After a string of defeats, he still refused to pay me for peace. Thankfully, though, the UN stopped the war.
Holed up in my own territory, I was now eight turns away from the stasis chamber, but every turn counted. The part was being built in my biggest production city, which was heavily lumbermilled. I diverted all my workers to that city to chop-rush (which you can do, but makes no sense-- wooden spaceship parts??). My production city was significantly weakened, but the ship launched and, one way or another, it wasn't going to matter any more.
I hit shift-enter, just to make the turns go by faster. His last city was only a few thousand away from legendary culture and growing fast. It was deep inland, so unsackable. If he spawned a great artist before the ship landed, he would win. If he didn't, I would win.
And he...... didn't.

. I won, just three turns before the enemy's last city would have gone cultural. My economy is a basketcase, I don't know archery, flight, divine right, or horseback riding, my production city is in shambles... but I won.

.