Although NASA did not beat the Russians at this feat (they launched their first station in 1971), there was no pressure on NASA to beat the Russian's in heavy lifting which is all launching a space station proves.
The launch on Skylab was the final launch of the American Saturn V rocket which had been used during the Apollo program. The station was launched in a single launch and upon reaching orbit the solar panels unfolded.
Unfortunately, the Skylab program had serious problems from the moment the rocket lifted off the launch pad. About one minute into the launch, the heavy virbrations from the rocket caused one of the solar panels to be ripped off of the station taking with it part of the outer hull. This included a section that protects the cabin from a lot of the suns energy. Although there was no breach in the hull, it did cause power shortages and made it very hot in the crew cabin.
Amazingly, a simple fix was quickly developed which involved the first crew deploying a milar cape over the section of missing hull to reflect sun energy. The station would also be reoriented to so the remaining solar panels could be as efficient as possible. This solved the power issues.
During its time in orbit, Skylab was manned by three crews (each containing 3 astronauts). The USSR set endurance record of 24 days was broken by the first crew of the station and that record would eventually be pushed up to 84 days by Skylab's final crew in 1974.
Despite some later dissapointments-the station was intended to be reactivated for the shuttle program but its orbit decayed too fast and the shuttle was delayed-Skylab is considered a very succiessiful program.
In July of 1979, Skylab made an uncontrolled reentry over the Indian Ocean and Western Australia causing a temporary worldwide scare.
You can see the milar cape in this photo as well. Also, notice the mission solar panel to the botton left. There should be one to match the one on the right.
I love hearing of close shaves and improvisations. Especially in space! 
