Brazil have already having qualified for next year's finals in Russia while second-bottom Bolivia are out of the running for one of South America's qualifying places.
The visitors had the best in a match played at high altitude and searing heat on a poor pitch that made neat play difficult.
Lampe made several fine saves, particularly in the first half when he twice denied Neymar from close range and then kept out a point-blank shot from Gabriel Jesus.
The keeper thwarted both players again in the second period, after Bolivia's Diego Bejarano Ibanez rattled the bar in first-half injury time with a spectacular 30-metre strike.
"We created lots of chances but the goalkeeper had a happy afternoon, he deserves our congratulations," Brazil's captain for the day Casemiro said after the game.
Brazil lost Thiago Silva to injury after 28 minutes but were never in danger of losing their first competitive match since Tite took over as coach in June last year.
The point extended his run in the qualifiers to 11 games without defeat. Brazil top the South American standings with 38 points from 17 games, while Bolivia have 14 points
Brazil are the only team to have played in every World Cup since the first tournament was held in Uruguay in 1930.
(Reporting by Andrew Downie; editing by Ken Ferris)
