Drake was very much in his feelings as he discovered that the Backstreet Boys would be performing at his 40th birthday ... and video shows him totally geeking out while singing alongside the legendary boy band.

In one clip ... the rapper exclaimed, "Oh my God," as the Backstreet Boys walked on stage ... before smiling wildly, laughing and pointing at the boy band as they took the stage.

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In another clip obtained by TMZ ... Backstreet Boy Kevin Richardson described how he connected with the rapper before this special performance as the rapper embraced the bandmates.

And finally ... Drake joined the boy band in singing their hit song "I Want It That Way."

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We reported earlier ... Drake's birthday party at NYC's Casa Cipriani was the stuff of legends.

There was a luxury giveaway, a "Deal or No Deal"-style game with prizes up to $1 million, and so much more.

In another clip obtained by TMZ ... Drake spoke out about the importance of paying it forward ... and pay it forward he did last night!