Bryant, who was named the Western Conference Player of the Week on Monday, has scored at least 40 points for nine straight games, matching the best such run of Jordan’s career, set during the 1986-87 season.
Wilt Chamberlain holds the NBA record with 14 straight games with at least 40 points. He set the mark during the 1961-62 campaign.
Bryant scored 41 points in the Lakers’ 106-101 home triumph over Seattle on Sunday but apologized to his teammates for forcing several shots late in the contest when he was stuck at 39 points.
Shaquille O’Neal added 27 points and 17 rebounds for the Lakers, who have won four games in a row and 18 of their last 24 to move into seventh place in the Western Conference playoff race.
Lakers coach Phil Jackson had a kidney stone removed on Monday and may not man the bench for the team against the Clippers on Tuesday. He has never missed a game in his coaching career.
The Clippers have lost 10 of their last 13 contests, including an 89-87 setback to Atlanta on Saturday.
Trailing by two points, Los Angeles had a pair of opportunities in the final 10 seconds. But Lamar Odom and Brand was smothered by multiple defenders as he tried put home the rebound for the tying hoop.
The Clippers shot just 4-of-19 from the arc and 9-of-13 from the line.
The Lakers have won the first two meetings between the teams this season, one of which was considered a road contest. The Lakers are 20-2 against the Clippers since the start of the the 1997-98 season.
The Clippers are 1-6 as the road team against the Lakers in the Staples Center.