It is clear that salvation is from God. God is called Savior in the Old Testament and Jesus is Savior in the New Testament. Further, the New Testament words of Jesus makes it clear that all of Scripture is really about Christ.
Luke 24:25-27 (KJV)
25 Then he said unto them, O fools, and slow of heart to believe all that the prophets have spoken: 26 Ought not Christ to have suffered these things, and to enter into his glory? 27 And beginning at Moses and all the prophets, he expounded unto them in all the scriptures the things concerning himself.
If, then, God is Savior, and Jesus is the path to salvation, and the entirety of Scriptures are about Jesus, then Jesus, being God, is Savior in the Old Testament as well. Further, it is clear that all of Scripture defines salvation as belief in God. Our verses above from John demonstrate this fact for the New Testament. The proof text for the Old Testament is Genesis 15:6:
And he believed in the LORD; and he counted it to him for righteousness.
Paul addresses this entire issue in Romans 4. Having declared the Jewish nation just as sinful as the Gentiles (Romans 2-3), Paul turns to the question that should have absorbed the typical Jewish reader. The question (Rom 4:1) might be better understood if we state it this way: Our Father Abraham came before the law. How was he justified? Was he justified by the law? This is obviously a serious question. Abraham is clearly the Father of the Jewish nation. From this patriarch they all trace their heritage. Or, as the NIV phrases it, what did Abraham discover in this matter?
Paul has just argued that the Israelite is as sinful as the Gentiles they have always looked down upon. Yet, says Paul, mere obedience to any form of the law will not justify one in the sight of God. Where, then, does Abraham sit in this argument? For, it should seem apparently that the Jewish nation sits where Abraham sits.
The point Paul will make is that Abraham was not saved because of his works. The patriarch was saved because of or on account of his faith. This would have been a startling message to the Jews of Paul's day. Abraham becomes the proof of what Paul has just taught at the end of Romans 3. Abraham was justified by faith!
The Jews have always been prideful of Abraham. This pride is properly placed if Abraham has done something to earn his salvation. After all, Abraham packed up and moved out when called upon by God. Is not this a work? Was it not the fact that Abraham obeyed and acted that causes God to justify him?