The sides were close throughout, and the scores were level with just over a minute remaining, after Davis had kept the Pelicans ahead throughout the final period, but a run of late free throws ensured that the home side saw out the win.
The Brooklyn Nets put their defeat to the Boston Celtics earlier this week behind them as they clinched victory in the second meetings between the two sides in three days.
The Nets opened up a 22-point lead in the second quarter, before Isaiah Thomas and Avery Bradley got the visitors back into the game, but Jarrett Jack saved 13 of his 22 points for the final 12 minutes to ensure that Brooklyn held on for the win.
Damian Lillard led the charge for the visitors, finishing the game with 30 points, while Kobe Bryant struggled as he tried to get the Lakers back into the game, making just six of his 22 shots from the field.
Results in full: Toronto Raptors 91-80 Los Angeles Clippers, Boston Celtics 101-111 Brooklyn Nets, Phoenix Suns 116-122 New Orleans Pelicans, Dallas Mavericks 114-117 Oklahoma City Thunder, Golden State Warriors 118-105 Denver Nuggets, Portland Trail Blazers 107-93 Los Angeles Lakers