Epps, who also grabbed a career-high 16 rebounds, put the Tigers (5-2) ahead by six points on a 3-point play with 57 seconds remaining. Rob Gray pulled the Cougars within three points at 80-77 on a 3-pointer less than 10 seconds later.
Following an LSU turnover, Houston (8-2) had a chance to tie it, but the 5-foot-11 Waters blocked Corey Davis Jr.'s 3-point attempt with six seconds to play. Devin Davis missed a long 3-point shot at the buzzer for the Cougars.
Waters had 17 points and six assists to go along with his first blocked shot of the season for the Tigers, who never trailed during the final 6 1/2 minutes. Mays had 18 points and a career-high nine rebounds.
Gray and Corey Davis Jr. scored 20 points apiece for Houston, whose winning streak ended at seven games. Devin Davis had 14 points.
LSU: The Tigers extended their winning streak to three games with the tightly-contested victory. LSU won its other close game this season, edging Michigan 77-75 in Hawaii.
Houston: The Cougars fell short in their bid for their longest winning streak in 10 seasons. For the first time this year, Houston was outrebounded 38-33.
LSU will continue its six-game homestand when it faces Stephen F. Austin on Saturday.
Houston returns home to meet Prairie View on Sunday.