The Bees twice came from behind before Yoane Wissa beat Bournemouth goalkeeper Kepa for the winner on the hour mark.
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Frank later said, "It was crazy, I must admit.
"The first 20 minutes, Bournemouth were better than us. We gave them the first goal - sometimes that happens - they had a few other chances but, after that, we scored a good goal and we grew into the game.
"In the second half, we were the only team on the pitch - we were clearly better. We created and scored two fantastic goals and kept Bournemouth to the bare minimum.
"I am very happy."