Cliff Lee was the star of the Texas - Tampa Bay American League Divisional Series. He won two games, pitched 16 innings and struck out 21. But more impressive that any of those statistics is the fact that he WALKED ZERO.
It should be pretty easy to figure out that when you work ahead in the count and do not allow free bases, good things will happen. A pitcher, no matter the level, is not going to throw a no hitter every time he takes the mound. The nature of the game is that the opponent will get base hits. But, by not allowing free base runners in front of those hits, you minimize the damage the hits can make.
When you get ahead in the count by throwing strikes on the first pitch and two of the first three pitches, you put the hitter in a defensive mode. He isn't as confident and is more likely to guess at what pitch is coming next. Many of the Rays' hitters on Tuesday night struck out on pitches where they looked totally clueless - a side effect of guessing.