Lampard nodded home a 50th-minute cross from Branislav Ivanovic but the visitors were forced to hang on with Ivanovic heading against his own crossbar with four minutes to go.
After last week's high-octane 5-3 defeat to Arsenal at Stamford Bridge, Villas-Boas welcomed a first half of "low intensity" and said the points were all important.
"We are very happy because we needed this stimulus of a win before the international break to make sure everybody goes into the break with a better feeling," Villas-Boas said.
"It (the clean sheet) was important. It is always important to win the game, no matter what are the conditions. We had to suffer a little bit but we managed to hold onto a clean sheet.
"It is never easy at Ewood Park, particularly when you are going through back-to-back defeats in the Premier League and bearing in mind that Blackburn are in desperate need of points."