Chayei Sara

Avraham sends his servant Eliezer back to his hometown to find a wife for his son. Eliezer takes ten camels and heads out. When he arrives he stops at the well & says a prayer, asking Hashem to send him the right girl for his master's son. Then the posuk states ויהי הוא טרם כלה לדבר , & it was when he had not yet finished speaking והנה רבקה יוצאת that suddenly Rivka came out.

The Ben Ish Chai asks, why does it say the word הוא? It appears that it's superfluous. It could have just said ויהי טרם כלה לדבר , & it was as he finished speaking. He answers that the Torah wants to emphasize Eliezer's prayer. The Midrash tells us there were three people who were answered right away & one of them was Eliezer. Not only that, but eliezer was the first one to be answered immediately. After him came Moshe Rabainu & then Shlomo Hamelech.
Since he was the first person in history to have his prayer answered immediately, it says הוא, this one. Eliezer, who was the first one in the world to be answered right away, didn't even complete his prayer, and was answered.  

What was so special about Eliezer's prayer that the Torah has to make a point to tell us that he was the first to be answered?

There's a story that's brought by the ברכי נפשי about רב משה אהרן שטרן the mashgiach of kaminenetz. He said that his grandfather רב יעקב יוסף הרמן was once dealing with a shidduch & was in a quandary not knowing which way to go. Either they would break it off or go full force. One morning he came to the Kotel & poured his heart out davening fervently for a hint from above on how to proceed. As he's davening, one of the papers that were in the cracks of the Kotel came & rested at his feet. He picked it up & it was a page from the siddur, that said וארשתיך לי לעולם , I will betroth you to me forever. Needless to say the shidduch went through.

The ברכי נפשי says that we see from here how a prayer that comes from the recesses of your heart can bring supernatural results. Such is the power of prayer.

This works even for simple things. There's a story told about רב פנחס מקוריץ whose students heard him saying at the end of shemona esrai יהי רצון מלפניך שהמשרתת תחזור ,may it be your will that the helper returns. His students, who were sure that this was some kind of lofty prayer went looking into all the seforim on davening to find what this one was for but to no avail. They couldn't find it anywhere. They asked their rebbi, what's the meaning behind that prayer you said at the end of davening? The rebbe explained that there was really nothing hidden about it, rather he was simply praying that the nurse that his wife had had for many years who was now leaving would come back because his wife was weak & really needed her. The students learned from him that no matter what you need or how mundane it is you can ask Hashem for it.  

Perhaps this is what the Torah was teaching us by stressing that Eliezer's was the first prayer to be answered. His was the first prayer that really came from the heart to teach us that when we really want something, no matter how big or small, we can ask Hashem for it. If we really pray from the heart & mean it then hopefully we too will be answered instantly!