Gasol hauled down 10 rebounds while Bryant logged a three-point play with just over 1 minute remaining to help nail down the Lakers' fifth win in six outings.
Los Angeles emerged with the victory after the Pistons were unable to score on a pair of opportunities over the closing seconds.
Detroit got 20 points and 12 rebounds from Greg Monroe but couldn't avoid its third loss in four games.
Will Bynum added a double-double of 18 points and 10 assists in the Pistons' defeat.
Celebrity Families of 2014 [PHOTOS]