or prevailed over so that people would put their trust in Him.

My guess is that this is a comment about God's sovereign control over all events and His capacity to move within/in spite of those events to accomplish His purposes.

reversing or overturning the events to show His dominance

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Note added at 3 hrs (2009-10-17 18:34:02 GMT)
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p.s. I think it might be "maNy years ago"?

‘Overrule’ is without doubt an appropriate word here, and is widely used in this sense by Bible-believing Christians.

‘Overrule’ refers to the sovereignty of “him who worketh all things after the counsel of his own will” (Eph. 1:11). This overruling extends to God’s direction of human action: “The king’s heart is in the hand of the Lord, as the rivers of water: he turneth it whithersoever he will” (Prov. 21:1); “The Lord hath made all things for himself: yea, even the wicked for the day of evil” (Prov. 16:4).

The classic references in this respect are Genesis 50:20: “But as for you, ye thought evil against me; but God meant it unto good” and Genesis 45:8: “So now it was not you that sent me hither, but God”. This overruling influence of God in Daniel’s life is seen at the outset of the book of Daniel in the conquest which led to Daniel’s captivity: “...came Nebuchadnezzar king of Babylon unto Jerusalem, and besieged it. And the Lord gave Jehoiakim king of Judah into his hand” (Dan. 1:1b-2a). In the sentence given in the question, ‘overrule’ means that while Daniel’s enemies, in having him cast into the den of lions, intended to do evil, God permitted this and used the events for His own purpose – the greater good to which Mrs Masters refers by citing Romans 8:28.