Finn and Rachel were at Mr. Shue's reception. Even though Mr. Shue's day was ruined doesn't mean Finn and Rachel's day had to be. Right after Finn told Rachel "We are endgame", they headed their way to the stage. The music started and they started to sing. Even though it would be hard because they both have strong musically chemistry, they both only wanted to sing together. Nothing else.
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As the song progressed so did their feelings. First their eyes just intimately met. That led to them holding hands. At the point they couldn't help themselves. When the song ended, they made their way up to their hotel room. It was kinda funny because they also saw 4 other couples in the hallway going to tier room at the same time. But they just let their feelings go at it.