McNeil finished with 11 points and 11 rebounds and Brown had 10 points and 10 rebounds for the Cougars (6-3).
Houston led 59-53 with 5:06 to play before Nevada scored five straight to make it a one point game. The Cougars pushed their lead back to four, but the Wolf Pack rallied again.
With his team down 62-60 and 34 seconds remaining, Jordan Finn went to the line for two foul shots but made just one.
Brown added two free throws for the final margin.
Kevin Panzer had 11 rebounds to help Nevada outrebound Houston 53-35.