Reagan won on pretty much a single issue: the hostages.

The fact that American Citizens had been held hostage in Iran for over a year, and Carter had bungled the rescue attempt, was what sunk him. The Iranian Oil Embargo came out of that event, because it would be pretty shitty to give monetary support directly to a country that was holding our citizens hostage, eh?

Then the Carter Administration was getting close to a deal with the Iranian captors, but the Reagan camp met with the Iranians and urged them to hold off until after Reagan was sworn into office, because they'd have a much more sympathetic administration in place (plus it would be an immediate feather in his cap). So they did.

And the best part, the Iranians released the hostages on Reagan's Inauguration Day. Talk about a sucker punch. What should have been a day dedicated to talking about our new president instead became all about the hostages being released. It was like "Ronald Reagan who?". Nobody ever investigated how suspicious that was though. Weird.

This was also the beginning of the whole Iran/Contra affair, his first day in office.