I agree that the final judgment is according to works. We are justified—made right with God and given a title to heaven—by faith alone apart from works. This faith, though, always and necessarily leads to good works, such that at the final judgment works can be necessary as evidence that we have already been accepted by God. So works are necessary as evidence, not basis.

One analogy may be going to a concert. When you are going to a concert you buy a ticket. Then, to get into the concert, you have to bring the ticket. But the ticket is not what gave you the right to get in. Paying the money is what gives you the right. The ticket is the evidence that you paid, that you bought entrance into the concert. It's necessary, but the piece of paper is not why you are able to get in.

Likewise, our right to enter the kingdom on the last day was purchased by Christ's death. Our works are evidence that he has purchased us, since all whom he purchased are not only justified, but also sanctified. But our works aren't what give us the right. They show that we possess that which does give us the right—namely, Christ.

However, there is still something missing most of the time when we articulate the necessity of works at the final judgment, even when we seek to be clear on the difference between basis and evidence. And it's this: The only reason your works are able to function as evidence is because your works themselves have been justified in Christ.

In other words, Christ justifies not only our persons, but also our works (see 1 Peter 2:5).[1] It is only justified works that can serve as evidence of our right standing with God on the last day.

Which only serves to underscore, once again, God's grace and the truth of justification by faith alone. Yes, works are necessary on the last day as evidence that we have been justified apart from works. But our works are only able to serve as evidence because they have themselves been made acceptable to God in Christ, apart from our doing of any works. For your works cannot be justified by works—that would be a contradiction in terms.

[1] Sorry for a footnote in a blog post! Here's what I also wanted to say there: you also see this several places in Revelation—including, interestingly, the description of the final judgment, if you read it closely (and which I have a post on that I may put up).