Klaassen was unmarked at the back post to tuck away Memphis Depay's corner after 19 minutes, and while the Dutch did dominate with almost relentless attacks in the closing 20 minutes. Louis van Gaal's side was unable to win by a larger margin.
Stefan de Vrij and Depay both sent good chances wide in the second half while, at the other end of the field, Dutch goalkeeper Justin Bijlow made an important save from Igors Tarasovs following a corner in stoppage time.
It was a third win in four games for the Dutch since Van Gaal returned as coach and they are expected to move closer to World Cup qualification when they host Gibraltar in Rotterdam on Monday (stream LIVE on ESPN+).
Latvia remained on five points with a single win from their seven qualifying group games.