I think you may be correct that the word "Sabbath" may be used for the first time in Exodus 20, but let me get some things done today and I'll show that the Sabbath was known prior to that time.
Very fair question. 
Actually, the word "Sabbath" shows up on the NKJV in Exodus chapter 16.
Genesis 2:1-4 “Thus the heavens and the earth, and all the host of them, were finished. And on the seventh-day God ended His work which He had done, and He rested on the seventh-day from all His work which He had done. Then God blessed the seventh-day and sanctified [made the day holy] it, because in it He rested from all His work which God had created and made.”
I can’t imagine that God required any form of rest, mental, emotional or physical, so it is logical that He rested as an example of what He wanted us to do. The example is for us to rest from our weekly activities.
Mark 2:27-28 “And He said to them, ‘The Sabbath was made for man, and not man for the Sabbath. Therefore the Son of Man is also Lord of the Sabbath.’”
This text comes up often to prove that man is not bound by the Sabbath, but I believe that it really means that the Sabbath was made for us to be a blessing.
Genesis 8:10-12 “And he waited yet another seven days, and again he sent the dove out from the ark. Then the dove came to him in the evening, and behold, a freshly plucked olive leaf was in her mouth; and Noah knew the waters had receded from the earth. So he waited yet another seven days and sent out the dove, which did not return again to him anymore.”
This text doesn’t specifically reference the Sabbath or a sanctified holy day, but it does indicate that the weekly cycle from creation was still being followed.
Exodus 16:4 “Then the Lord said to Moses, ‘Behold, I will rain bread from heaven for you. And the people shall go out and gather a certain quota every day, that I may test them, whether they will walk in My law or not. And it shall be on the sixth day that they shall prepare what they bring in, and it shall be twice as much as they gather daily.’”
Exodus 16: 22-23 “And so it was, on the sixth day, that they gathered twice as much bread, two omers for each one. And all the rulers of the congregation came and told Moses. Then he said to them, ‘This is what the Lord has said, “Tomorrow is a Sabbath rest, and holy Sabbath to the Lord. Bake what you will bake today, and boil what you will boil; and lay up for yourselves all that remains, to be kept until morning.”’”
Exodus 16:25-30 “Then Moses said, ‘Eat that today, for today is a Sabbath to the Lord; today you will not find it again in the field. Six days you shall gather it, but on the seventh day, the Sabbath, there will be none.’”
Exodus 16 makes it very clear that the Sabbath was know prior to the Ten Commandments being given at Sinai. God performed a miracle every day for 40 years to feed Isreal with manna. Five days a week the manna appeared on the ground and spoiled over night, but on the sixth day they were instructed to gather twice as much because it didn’t not appear on the seventh day and it did not spoil.
