What is the higher power of Buddhism?

It depends largely on what tradition of Buddhism is being practiced. There is a higher power in Buddhism, it is represented differently by different schools.

Fundamentally in Buddhism we take refuge in the Buddha, Dharma and Sangha. The Buddha was a man who attained enlightenment and taught others. He was a teacher and his teachings are referred to as the Dharma. The Sangha are his students-monks and nuns-who have dedicated all of the energy in their life in order to preserve the teachings (Dharma) and make them available to future generations.

In the book "The Foundation of All Good Qualities" by Venerable Geshe Tsultrim Gyelsten I found this:

The foundation of all good qualities is the kind Guru
Cultivating the Guru properly is the root of the path
Realizing this clearly with great diligence,
Bless me to rely on the Guru with highest devotion

Also he goes on in the book to list the qualities of a good teacher and the qualities of a good student.

Six Attitudes of a Student:
# To view ourselves as a critically ill person # To view the teaching that is being offered to us as a treatment for our illness. # To view the teacher as a skilled doctor. # To understand that if we practice the Dharma diligently it will cure our illness, but that we will need to seek this treatment for a great length of time in order to make a full recovery. # To view the Buddha as a holy being. # To wish for the teachings to endure in the world for a long time. We should always hold the Dharma in very high esteem like a sick person regards the medicine that treats their illness as their salvation. As a sick person takes refuge in their medications, so we need to learn to value the Dharma. And we need to rely on highly skillled physician like teacher to lead us on the path. The source of the Dharma is the tathagatas, and this is why we regard the buddhas as holy beings because it is from the buddhas that the Dharma originated.

From Hui Neng's commentary on the Diamond Sutra translated by Thomas Cleary on p.99:

Subhuti said to the Buddha, 'World Honored One, will anyone who gets to hear this exposition develop genuine faith?'

Subhuti is asking, 'This teaching is very deep, hard to believe, hard to understand, the intelligence and insight of ordinary people of the final age are slight and inferior-how can they believe in it? The Buddha replies as follows.

Buddha told Subhuti, Don't talk that way, in the last five hundred years after the death of the Realized One, there will be those who keep the precepts and do good deeds who will be capable of conceiving belief in this exposition, considering it to be true. You should know that these people will have planted roots of goodness, not with one, two, three, four, or five buddhas, but with infinite thousands of myriads of Buddhas. They will conceive pure belief on hearing this exposition even for a moment.

But the Buddha is not a god or person that expects us to blindly accept what he says. Any good teacher would want you to practice what he teaches and see if it applies to your life and helps you.

For example, here are two quotes from the Dhammapada I found on the topic:

Gripped by fear men go to sacred mountains, sacred groves, sacred trees and shrines. (Dhammapada 188)

No one saves us but ourselves
No one can and no one may
We ourselves must walk the path
But Buddhas clearly show the way.
(Dhammapada 165)

From the Upali Sutta verse 16:

"Investigate thoroughly, householder. It is good for such well-known people like you to investigate thoroughly."

"Venerable Sir, I am even more satisfied and pleased with the Blessed One for telling me that. For the other sectarians, on acquiring me as their disciple, would carry a banner all over Nalanda announcing: 'The householder Upali has come to discipleship under us.' But on the contrary, the Blessed One tells me: 'Investigate thoroughly, householder. It is good for such well-known people like you to investigate thoroughly.' So for the second time, venerable sir, I go to the Blessed One for refuge and to the Dhamma and to the Sangha of Bhikkus. Let the Blessed One remember me as a lay follower who has gone to him for refuge for life."