Objection 1. It would seem that Christ did not work miracles by Divine power. For the Divine power is omnipotent. But it seems that Christ was not omnipotent in working miracles; for it is written (Mark 6:5) that "He could not do any miracles there," i.e. in His own country. Therefore it seems that He did not work miracles by Divine power.
Objection 2. Further, God does not pray. But Christ sometimes prayed when working miracles; as may be seen in the raising of Lazarus (John 11:41-42), and in the multiplication of the loaves, as related Matthew 14:19. Therefore it seems that He did not work miracles by Divine power.
Objection 3. Further, what is done by Divine power cannot be done by the power of any creature. But the things which Christ did could be done also by the power of a creature: wherefore the Pharisees said (Luke 11:15) that He cast out devils "by Beelzebub the prince of devils." Therefore it seems that Christ did not work miracles by Divine power.
On the contrary, our Lord said (John 14:10): "The Father who abideth in Me, He doth the works."
I answer that, as stated in I, 110, 4, true miracles cannot be wrought save by Divine power: because God alone can change the order of nature; and this is what is meant by a miracle. Wherefore Pope Leo says (Ep. ad Flav. xxviii) that, while there are two natures in Christ, there is "one," viz. the Divine, which shines forth in miracles; and "another," viz. the human, "which submits to insults"; yet "each communicates its actions to the other": in as far as the human nature is the instrument of the Divine action, and the human action receives power from the Divine Nature, as stated above (Question 19, Article 1).
Reply to Objection 1. When it is said that "He could not do any miracles there," it is not to be understood that He could not do them absolutely, but that it was not fitting for Him to do them: for it was unfitting for Him to work miracles among unbelievers. Wherefore it is said farther on: "And He wondered because of their unbelief." In like manner it is said (Genesis 18:17): "Can I hide from Abraham what I am about to do?" and Genesis 19:22: "I cannot do anything till thou go in thither."
Reply to Objection 2. As Chrysostom says on Matthew 14:19, "He took the five loaves and the two fishes, and, looking up to heaven, He blessed and brake: It was to be believed of Him, both that He is of the Father and that He is equal to Him... Therefore that He might prove both, He works miracles now with authority, now with prayer... in the lesser things, indeed, He looks up to heaven"--for instance, in multiplying the loaves--"but in the greater, which belong to God alone, He acts with authority; for example, when He forgave sins and raised the dead."
When it is said that in raising Lazarus He lifted up His eyes (John 11:41), this was not because He needed to pray, but because He wished to teach us how to pray. Wherefore He said: "Because of the people who stand about have I said it: that they may believe that Thou hast sent Me."
Reply to Objection 3. Christ cast out demons otherwise than they are cast out by the power of demons. For demons are cast out from bodies by the power of higher demons in such a way that they retain their power over the soul: since the devil does not work against his own kingdom. On the other hand, Christ cast out demons, not only from the body, but still more from the soul. For this reason our Lord rebuked the blasphemy of the Jews, who said that He cast out demons by the power of the demons: first, by saying that Satan is not divided against himself; secondly, by quoting the instance of others who cast out demons by the Spirit of God; thirdly, because He could not have cast out a demon unless He had overcome Him by Divine power; fourthly, because there was nothing in common between His works and their effects and those of Satan; since Satan's purpose was to "scatter" those whom Christ "gathered" together [Cf. Matthew 12:24-30; Mark 3:22; Luke 11:15-32].
Source: Summa Theologica (New Advent)