The Clippers pulled to within 58-55 at 67 seconds into the third quarter but New Orleans responded with a 12-1 run to put the game away, capped by a 3-pointer from David Brown, who finished with 16 points for the Hornets.
Bower, the Hornets' general manager, took over the coaching duties last week for Byron Scott, who was fired.
Peja Stojakovic scored 15 points for the Hornets, who were again without guard Chris Paul, who sprained an ankle in Friday's game against Portland.
Al Thornton poured in 30 points and Baron Davis added 23 for the Clippers, who lost for the fourth time in five games.
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