Jesus gave the Apostles the power to perform miracles. Not only that, we have this testimony about the early church:

(1 Corinthians 15:3-8 NIV) For what I received I passed on to you as of first importance : that Christ died for our sins according to the Scriptures, {4} that he was buried, that he was raised on the third day according to the Scriptures, {5} and that he appeared to Peter, and then to the Twelve. {6} After that, he appeared to more than five hundred of the brothers at the same time, most of whom are still living, though some have fallen asleep. {7} Then he appeared to James, then to all the apostles, {8} and last of all he appeared to me also, as to one abnormally born.