The Lakers' defence in the first quarter was "terrible", Davis said afterwards, but it mattered little as the 26-year-old finished the half with 26 points poured in from all over the court.
Caris LeVert racked up a huge 51 points as the Brooklyn Nets triumphed 129-120 against the Boston Celtics.
The guard entered the final quarter with only 14 points to his name, but a late flurry saw him achieve career-high figures in the overtime win.
The Nets had been 17 points behind after three quarters of the game at TD Garden.
Elsewhere, the Sacramento Kings finished as 133-126 winners over the Washington Wizards, the Denver Nuggets fell 116-100 to the Golden State Warriors and the Minnesota Timberwolves beat the New Orleans Pelicans 139-134.
The Phoenix Suns gave up a 17-point lead to lose 123-114 at home to reigning champions the Toronto Raptors, the San Antonio Spurs edged the Charlotte Hornets 104-103 and the Los Angeles Clippers beat the Oklahoma City Thunder 109-94.