From StrategyWiki, the free strategy guide and walkthrough wiki

To get to the secret exit, get a blue Yoshi in the beginning. Other Yoshis won't work, because a vine has to be climbed. Keep him until you see the key near the end. Use him to grab and hold the key in his mouth, then walk into the keyhole. This leads to Star Road, and the real exit is not too far, just two jumps and you're done.