After the first two picks tallied with expectation - the Kansas City Chiefs and the Jacksonville Jaguars took left tackles Eric Fisher and Luke Joeckel respectively - Miami brokered a deal with the Oakland Raiders.
The Dolphins sent their first selection this year, pick 12, as well as a second rounder - number 42 - to the Raiders and chose Jordan.
Many expected Miami, who also made a splash in free agency with the additions of wide receiver Mike Wallace and linebacker Dannell Ellerbe among others, to choose tackle Lane Johnson.
The Oklahoma standout was subsequently chosen next by the Philadelphia Eagles, with the top five being rounded off when the Detroit Lions added edge rusher Ezekiel Ansah.
Meanwhile, Manchester-born Menelik Watson was not selected in the first round of the 2013 NFL Draft.
Watson, who overcame an impoverished childhood in Longsight before heading stateside via the Canary Islands, was expected to be taken on the opening day of three at New York's Radio City Music Hall.
The offensive tackle, from Florida State, will now have to wait until tomorrow when his name will almost certainly be called in round two.
While not being snaffled at this stage may be something of a disappointment, a second-round berth would still be a considerable achievement for someone who did not know the sport's rules two years ago.