How was Abraham able to rescue Lot? Trouble began (in Genesis) when the Kings of Sodom and Gomorrah (and their allies) rebelled against their overlord, Chedoloamer, who swept down on them with an avenging army, killing or capturing everyone they could get their hands on, including Abraham's nephew Lot. 

Genesis 14:14: "And when Abram heard that [Lot] was taken captive, he armed his trained servants, born in his own house, three hundred and eighteen, and pursued them unto Dan."

How was it that Abraham's private army of 318 was more than a match for the presumably thousands that accompanied the victorious enemy king? Was it because the enemy was too heavily laden with the spoils of war?

Or was this one of God's miracle victories like Gideon against the Midianites where a few hundred men were allowed to defeat thousands?
No explicit reason for Abram's victory is given, but the surrounding context can give some clues:


  Genesis 14:8-11 ESV Then the king of Sodom, the king of Gomorrah, the king of Admah, the king of Zeboiim, and the king of Bela (that is, Zoar) went out, and they joined battle in the Valley of Siddim with Chedorlaomer king of Elam, Tidal king of Goiim, Amraphel king of Shinar, and Arioch king of Ellasar, four kings against five. Now the Valley of Siddim was full of bitumen pits, and as the kings of Sodom and Gomorrah fled, some fell into them, and the rest fled to the hill country. So the enemy took all the possessions of Sodom and Gomorrah, and all their provisions, and went their way. They also took Lot, the son of Abram's brother, who was dwelling in Sodom, and his possessions, and went their way.


Key facts:


Chedorlaomer's army had just finished doing battle (albeit victoriously) before kidnapping Lot. There may have been casualties, fatigue, POWs, issues with the treacherous lands, and whatever else.
The size of the Chedorlaomer's army (and his friends) isn't given.
They had just sacked a city and Abram executed a surprise attack at night. This can tip the scale.


With no further details about this we can surmise that this may have simply been a great victory against the odds. It might not have needed any miraculous intervention from God to happen--though I'm sure He helped:


  Proverbs 21:31 ESV The horse is made ready for the day of battle, but the victory belongs to the Lord.