Short simple answer:
if a fuel economy gain comes from
less friction inside the engine
or a faster burn in the cylinder that requires less degrees of ignition timing
then there is usually also a power increase too.
Recently, with many engines getting Variable Valve Timing, this feature usually adds better fuel economy 1500 to 2500 rpm and increased HP 3500 to 6500+ rpm.

Long answer

MPG
is for an entire vehicle
travelling on a specific road.

Horsepower for an engine
is usually used refering to a "peak" power
measured by a set of rules such as
SAE or Standard Dyno,
but can also be "instantaneous power" under different comditions.

Transmission/differential gearing
ties the engine to the vehicle
and certainly affects both
MPG and Torque at rear wheels.

If the pavement changes from
rough new blacktop to smooth old concrete
the MPG goes up,
but peak hp is unchanged.

If air temp goes up,
mpg goes up
but instantaneous power available goes down,
and so forth.

If a different gear is used
on a specific section of road
MPG may change
but peak rated HP is not.

To get away from such difficulties,
engineers create various styles of
maps,
comparing more than two things at once,
such as:

Power versus
RPM versus
Throttle Opening versus
Fuel Flow

Torque produced vs RPM vs Fuel flow

Perhaps the best such map
is the one that compares

Brake Mean Effective Pressure ( gives both Torque and HP)
versus
Average Piston Speed ( depends on rpm and crank throw)
versus
Fuel Consumption
expressed as mass of fuel used up during an hour of power produced,
which is called in techno-speak as
Brake Specific Fuel Consumption
or shortened to initials
BSFC

[Edit: See examples several posts down from this one]

While the above sounds complicated
it is a
"universal"
map that can be used to compare
engines of any size, stroke, cycles from
tiny weed whacker engines
to automotiveV8s
all the way up to
huge 100,000 HP ship engines

Any change that
improves fuel economy
in an area within such a
universal map
usually also improves
torque and HP
but only near that
specific piston speed.

At higher or lower
piston speeds
a change might cause
the BMEP to go up
but the BSFC may not
... could go up, down or stay the same.