So how did Lincoln accomplish this, through executive power or legislation?
Congress was not in session when Lincoln called up 75,000 troops to put down what he called rebellion and the seven Deep South states called secession. Lincoln called up this army by proclamation, a tool he used more than any previous President. Washington had issued the sole major proclamation prior to Lincoln when he declared the United States neutral in 1793.
Proclamations, like Executive Orders, are undefined in the Constitution and somewhat ambiguous.