When you search from the search box, iTunes narrows the matches in a Spotlight-like fashion, until, after no more matches are found, the particular song you typed in is the only one visible. This means you have to click on the previous playlist or your library to activate it again if you play the searched song.
Instead of using the search box when searching for a particular song, you can do so right inside the iTunes window. Make sure the song list window is active, then just type the song name. After a short delay, iTunes will automatically select the song, provided that it is in the selected playlist/library. And it doesn't eliminate the rest of the songs. Therefore, you can press Enter to play the song, and remain in your current playlist.
[robg adds: This "search in iTunes" is based on iTunes' ability to behave much like the Finder -- if you type an "F," iTunes will jump down to the first song that starts with "F." So if you know and can type the exact name of the song, the above method will indeed select it in an easier-to-use manner than does the search box. But if you're not exactly certain of the spelling, or if you don't recall whether you used "The" in front of the song name or not, you'll be better off with a real search via the search box.]

