The aggregate winner of the two-legged tie will compete in the top flight of Scottish football in 2014-15 and Terry Butcher's side will go into Sunday's return match at Easter Road with renewed confidence.
Hamilton made the early running but it was Hibs who created the opening chance of the contest, Scott Robertson hitting the post after 12 minutes with a 20-yard effort following some neat footwork and a cross from Sam Stanton.
The home side continued to press themselves but struggled in front of goal, with Mickael Antoine-Curier hooking an over-hit cross from James Hutchings over the bar.
Louis Longridge then spurned an excellent opportunity to give Hamilton the lead as he fired wide when well placed after Darian McKinnon had played him in.
That proved costly as Hibernian broke the deadlock on 39 minutes, Cummings scoring his first goal for the club having been given the chance to impress.
Cummings was offered the opportunity to shoot from 25 yards after the home defence had backed off, with the ball appearing to go through goalkeeper Kevin Cuthbert's hands.
The 18-year-old pounced again 10 minutes after the restart to score a classy second goal, with the striker showing composure to clip the ball over Cuthbert and into the net.
Hamilton defender Ziggy Gordon looked to have cleared the ball but the linesman sprinted back to the halfway line for the restart of the game and replays showed the ball was well over the line.
Hibernian goalkeeper Ben Williams came off his line to smother an angled drive from Andy Ryan before keeping out a shot in the closing stages from another substitute, Ali Crawford.
The Edinburgh side held on to secure their first away win of 2014 and will be favourites to remain in the Scottish Premiership come Sunday night.