No one is saying we are saved by works, it is God who saves. The question is can one be saved by faith alone or not. James clearly says no. This passages does "Not" support Luther's argument. You see, Luther was an Augustinian monk. He bought into the erroneous ideas of Augustine. As such Luther apparently didn't understand Paul's teachings correctly. Peter said many things that Paul wrote were hard to understand and they twist them to their own destruction. Luther was countering some errors in the Catholic church, but, as is often the case he went too far. Instead of getting back to the teachings of Scripture he went 180 degrees from the Catholic church on the issue of works.
We can see Paul's argument here in Ephesians 2:8 simply by reading this passage in context.
8 For by grace are ye saved through faith; and that not of yourselves: it is the gift of God:
9 Not of works, lest any man should boast.
10 For we are his workmanship, created in Christ Jesus unto good works, which God hath before ordained that we should walk in them.
11 Wherefore remember, that ye being in time past Gentiles in the flesh, who are called Uncircumcision by that which is called the Circumcision in the flesh made by hands;
12 That at that time ye were without Christ, being aliens from the commonwealth of Israel, and strangers from the covenants of promise, having no hope, and without God in the world:
13 But now in Christ Jesus ye who sometimes were far off are made nigh by the blood of Christ.
14 For he is our peace, who hath made both one, and hath broken down the middle wall of partition between us;
15 Having abolished in his flesh the enmity, even the law of commandments contained in ordinances; for to make in himself of twain one new man, so making peace;
16 And that he might reconcile both unto God in one body by the cross, having slain the enmity thereby:
17 And came and preached peace to you which were afar off, and to them that were nigh.
18 For through him we both have access by one Spirit unto the Father.
19 Now therefore ye are no more strangers and foreigners, but fellowcitizens with the saints, and of the household of God;
20 And are built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone;
21 In whom all the building fitly framed together groweth unto an holy temple in the Lord:
22 In whom ye also are builded together for an habitation of God through the Spirit.
(Eph 2:8-1 KJV)
When we look at the passage in context it becomes clear that Paul is making a distinction between the Jew and the Gentile. He tells the Gentile that they were aliens from the commonwealth and promises of Israel that they were without Christ and God, and so on. He goes on to explain how they have been brought into the commonwealth and promises, how they have been reconciled to God through Christ, etc. He says that has been done by Christ breaking down the middle wall of partition (the wall in the temple that separated Jews and Gentiles) and has abolished the commandments contained in ordinances, that is the Mosaic Law. The works spoken of in verse are the works of the Mosaic Law. Christ has abolished those ordinances contained in the Law, the ones the Jews kept to separate themselves from the nations.
A study the history of the time reveals the issue of the Judaizers which were a major problem in Paul's ministry. The Judaizers were Jews who were teaching Gentile believers that in addition to faith in Christ they also needed to keep the Mosaic Law and be circumcised. Knowing this was an issue in Paul's ministry sheds light on all of Paul's reaching on the issue of works. I would suggest that when you see Paul saying works don't save he's referring to the works of the Mosaic Law. He never says "Good deeds" aren't necessary for salvation. We can see the issue with the Judaizers dealt with in the Scriptures. All of Acts 15 deals with the issue of the Judaizers, it starts like this.
KJV Acts 15:1 And certain men which came down from Judaea taught the brethren, and said, Except ye be circumcised after the manner of Moses, ye cannot be saved. (Act 15:1 KJV)
We can also see it in Galatians.
KJV Galatians 3:1 O foolish Galatians, who hath bewitched you, that ye should not obey the truth, before whose eyes Jesus Christ hath been evidently set forth, crucified among you?
2 This only would I learn of you, Received ye the Spirit by the works of the law, or by the hearing of faith?
3 Are ye so foolish? having begun in the Spirit, are ye now made perfect by the flesh?
4 Have ye suffered so many things in vain? if it be yet in vain.
5 He therefore that ministereth to you the Spirit, and worketh miracles among you, doeth he it by the works of the law, or by the hearing of faith? (Gal 3:1-5 KJV)
It can be seen from Paul's words that someone was trying to convince the Galatians that they also needed to keep the Mosaic Law.
I'd invite you to research this; you'll find that Paul's teaching on works that don't save is address this issue of the Mosaic Law.