The 71 points tie for eighth most in NBA history. Donovan Mitchell of the Cleveland Cavaliers also scored 71 earlier this season. Only Hall of Famers Wilt Chamberlain (five times, high of 100), Kobe Bryant (81) and David Thompson (73) have scored more points in an NBA game, Reuters reported.
Lillard scored 41 of his points before the break, the most first-half points by a player in franchise history.
Jerami Grant added 13 points and Nassir Little scored 11 for Portland, which connected on 54.5 percent of its field goal attempts and was 20 of 39 from 3-point range.
Alperen Sengun had 17 points and 10 rebounds and Jae'Sean Tate also scored 17 points for Houston, which has lost nine straight games and 29 of its last 33.
Elsewhere, Anthony Davis scored 30 points with 15 rebounds and LeBron James added 26 points as visiting Los Angeles Lakers won the battle of dynamic duos with a 111-108 victory over Dallas Mavericks.
The Mavericks had Luka Doncic and Kyrie Irving on the court together for the fourth time, but fell to 1-3 with the newly-formed partnership. Doncic scored 26 points with nine rebounds, while Irving had 21 points and 11 assists.