They used parts of two songs from the show. The segment closed with the rousing title song, which wasn't surprising, and opened with one of the lesser-known songs, "I Cain't Say No," performed by one of the smaller characters, Ado Annie -- which was not only surprising, it was remarkable.
That's in theory. Once you saw the performance, the decision was understandable. The actress who sang “I Cain’t Say No” wasn't just terrific, she won the Tony as Best Featured Actress in a Musical, Ali Stroker. And it's not difficult to see why.
Her raise-the-roof performance (more than the title song) clearly has a much stronger country music arrangement. In part, I suspect that may be because they can’t do that as much with the title song, though they do stage it in more of a down-home country way.
Two comments on the songs. First, the background of "I Cain't Say No" is sung by a young woman who was gangly and awkward as a child, but grew up to be pursued by young man and now finds life a banquet. As for the second number, apparently they have audience members on stage during the show, so when you watch the video, that’s who the people are in the back.
Here then is Oklahoma! -- OK?
As a bonus, here is Ali Stroker's touching acceptance speech, the first performer in a wheelchair ever to win a Tony. Alas, the clip doesn't include the announcement of "and the winner is..." -- but it's worth it, regardless.