The truth of Jesus' resurrection prevailed over the lie that his corpse was stolen (and remained a corpse) due to the same way all of God's truth prevails - the Holy Spirit that raised Christ continued to work through all the Christians to spread the truth.
The Apostles were foremost, and exemplary, in promoting the truth of Jesus' resurrection. This emboldened all Christians to follow suit, and the main means of resisting the satanic lie was verbal.
Today we think that written publications and digital outlets are the best way of debating and presenting a case, either for, or against. But the situation back then was entirely different. The quickest way to promote Christ as risen from the grave was by believers witnessing verbally about Christ being the Son of God, with some 500 eyewitnesses to him being alive:
"[Christ] was buried, that he was raised on the third day according to
the Scriptures, and that he appeared to Peter, and then to the Twelve.
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. Then he appeared to James, then to all the apostles, and last
of all he appeared to me also." 1 Corinthians 15:4-7 N.I.V.
This was after the Holy Spirit came upon 120 Christians at Pentecost. After Peter's preaching, some 3,000 Jews and proselytes gathered in Jerusalem became Christians, convinced of the resurrection of the Son of God (Acts 2:30-43, do read all of it). Also, Acts 4:33 says that it was with great power that the apostles witnessed of the resurrection of the Lord Jesus.
Many more texts could be used to show the explosive nature of how the Holy Spirit empowered Christian witnesses to Christ's resurrection to impact not only the Jewish people, but the Gentiles. The Apostles led 'the charge', with their written accounts following years after many thousands of people had believed the testimony from hundreds of eye-witnesses.
The Apostles prevailed by the Holy Spirit empowering them (and hundreds of other witnesses) to keep telling the truth, that Christ was risen from the dead.