The whole point of a hybrid is to run the ICE only in its most efficient region. At low loads the electric battery drives the car. If the battery gets too low, then the ICE runs, but rather than running at a low (and inefficient) load, it runs at its sweet spot and the excess power it generates charges the battery. When the demand is high, rather than running the ICE hard, it is kept at its sweet spot and the electric motor boosts power instead.

So yes, the ICE part is more efficient in a hybrid, though it isn't magic.

The ICE is more efficient because the design constraints have changed.

Here's a single example with the Prius:

1. The intake valve stays open for part of the compression stroke.

2. (1) means that the compression ratio for the compression stroke is lower than the compression ratio for the power stroke.

3. The efficiency of the engine is limited by the compression ratio of the power stroke

4. The compression ratio of the compression stroke is limited by engine knocking (if you compress a mixture of fuel and air too much, it will spontaneously combust)

5. So this engine can be made more efficient than an engine that closes the valve for the entire compression stroke

6. Some (non-hybrid) engines have variable valve timing and can do (1) some of the time, to a small extent.

7. Doing (1) to a larger extent makes the low-RPM torque very poor.

8. Electric motors have excellent low-RPM torque, so (7) is compensated for by having an electric motor run at low speeds.

Somewhat, by putting an intermediate step between the gas/diesel engine and the work the engine can be run more efficiently as well, instead of having to speed up and down at the whims of the driver it can run at a more steady and constant pace and the electric engine also allows regenerative brakes to be used which can recapture a lot of the energy lost in a normal diving situation during braking.