The result has little impact on the CONMEBOL World Cup qualifying section with Brazil’s position as group winners already secure and Bolivia unable to improve on their spot in ninth.
Neymar, in particular, will be left cursing the performance of Lampe as the Huachipato goalkeeper prevented him from adding to his international tally of 52 goals with a series of impressive stops.
Gabriel Jesus, Willian and Dani Alves were also denied as the host held firm.
Bolivia offered little attacking threat but came close to scoring on the stroke of half-time when Diego Bejarano thumped a long-range drive against the crossbar.
Brazil, captained by Real Madrid’s Casemiro for the first time, appeared to struggle with the altitude in La Paz in the early stages and almost fell behind after 15 minutes.
Juan Carlos Arce’s corner was pulled back to Cristhian Machado on the edge of the penalty area and his well-struck shot arrowed narrowly past Alisson’s right-hand post.
The visitor had to wait until midway through the opening period for their first sight of goal and, unsurprisingly, it fell to the world’s most expensive player.
Neymar’s whipped effort from 25 yards looked destined for the bottom corner, but Lampe got down well to push it out for a corner.
The Paris Saint-Germain forward was in the thick of the action again soon after, as he took advantage of confusion in the home defence to bear down on Lampe but his shot was too close to the Bolivia goalkeeper.
The overworked Lampe was called into action again to keep out Jesus’ close-range effort after a clever flick from Paulinho.
Neymar was then somehow denied an opener in a thrilling passage of play just before the break.
After stumbling past the onrushing Lampe, the 25-year-old regained his footing to steer a powerful shot towards goal that was cleared by the head of Gabriel Valverde on the line. The ball fell back to Neymar and his second effort was once again cleared by Valverde, denying what would have been a certain goal.
Dani Alves then saw an audacious effort from 35 yards tipped over by Lampe, before Bejarano crashed a stunning effort from 30 yards against Alisson’s crossbar in what was a breathless end to the half.
The second half followed a similar pattern to the first with Lampe producing a breathtaking save just minutes after the restart to deny Paulinho, tipping the Barcelona midfielder’s acrobatic volley onto the post from Neymar’s deep cross.
Lampe continued to get the better of Neymar in their fascinating duel, first comfortably gathering his attempted lob and then superbly blocking his fierce close-range volley.
Fittingly, Lampe denied substitute Willian and Jesus in the closing stages to ensure the headlines would be his on a memorable day for the 30-year-old.