Paul wasn't writing that to today's Christians. He wrote it to the Ephesians. To people who were experiencing believing Jews coming from the church in Jerusalem and telling them, yes, you do need to have faith in Christ. But, you also need to be circumcised and keep the Law of Moses if you want to be saved. Read acts fifteen. It begins like this.
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.
2 When therefore Paul and Barnabas had no small dissension and disputation with them, they determined that Paul and Barnabas, and certain other of them, should go up to Jerusalem unto the apostles and elders about this question. (Acts 15:1-2 KJV)
This is the issue that Paul dealt with in his ministry. If you read Acts chapter 15 you'll see that the elders and Apostles had to address this issue.
22 Then pleased it the apostles and elders, with the whole church, to send chosen men of their own company to Antioch with Paul and Barnabas; namely, Judas surnamed Barsabas, and Silas, chief men among the brethren:
23 And they wrote letters by them after this manner; The apostles and elders and brethren send greeting unto the brethren which are of the Gentiles in Antioch and Syria and Cilicia:
24 Forasmuch as we have heard, that certain which went out from us have troubled you with words, subverting your souls, saying, Ye must be circumcised, and keep the law: to whom we gave no such commandment:
25 It seemed good unto us, being assembled with one accord, to send chosen men unto you with our beloved Barnabas and Paul,
26 Men that have hazarded their lives for the name of our Lord Jesus Christ.
27 We have sent therefore Judas and Silas, who shall also tell you the same things by mouth.1
28 For it seemed good to the Holy Ghost, and to us, to lay upon you no greater burden than these necessary things;
29 That ye abstain from meats offered to idols, and from blood, and from things strangled, and from fornication: from which if ye keep yourselves, ye shall do well. Fare ye well. (Acts 15:22-29 KJV)
This was a huge problem for Paul. It was such an issue that the Holy Spirit had him go to Jerusalem to settle it.
Then fourteen years after I went up again to Jerusalem with Barnabas, and took Titus with me also.
2 And I went up by revelation, and communicated unto them that gospel which I preach among the Gentiles, but privately to them which were of reputation, lest by any means I should run, or had run, in vain.1 (Gal. 2:1-2 KJV)
When Paul speaks of not being saved by works, he's speaking of the works of the Mosaic Law. It's even right there in the context of the Ephesians 2 from which you quoted.
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.1
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:1 (Eph. 2:8-16 KJV)
Paul explains what he means when he says you are not saved by works. He goes on to explain how Christ abolished the law of commandments contained in ordinances. That's the Mosaic Law.
