I am not an engineer, just thinking out loud here.
Does the addition of winglets delay the formation of wingtip vortices; thus decreasing the induced drag signature?
Any reduction in drag will increase performance and reduce power (fuel burn) for a given "V".
In the early 1990's, I owned a Cessna 150-J; there was a set of droop tips (elephant ears) on the aircraft. The stall characteristics were changed by this addition. These tips created an air dam stopping the higher pressure air under the outboard area of the wing from spilling over the tip to the lesser pressure top side. The wing become more efficient, because you had the use of all the wing area for lift. As a result the ailerons become more efficient also.