The visitors did not lay a glove on the Black Cats in the first half and saw their 2-0 first-leg advantage wiped out by goals from Ross Stewart and Charlie Wyke in front of a raucous home crowd of 9,971.
However in a much-improved second-half display, striker Hopper’s 56th-minute header calmed their nerves and although Lee Burge saved a Jorge Grant penalty, a 2-1 defeat at the Stadium of Light was enough to clinch a 3-2 aggregate victory and a showdown with Blackpool for a place in the Championship.
Sunderland, who now face a fourth season in the third tier, made the breakthrough arrived with just 13 minutes gone when Aiden McGeady crossed for Stewart to finish adeptly at the near post.
They should have been level on aggregate nine minutes later when the ball broke to Wyke inside the penalty area and although he rounded keeper Alex Palmer, he dallied and somehow managed to blast his shot at defender Timothy Eyoma as he raced back on to the line.
The home side’s high press was causing all kinds of problems for the Imps and their woes increased 12 minutes before the break.
McGeady once again provided the ammunition and this time it was Wyke who completed the job, stabbing home at the far post to make it 2-0.
Brennan Johnson saw a 40th-minute strike blocked by Bailey Wright as Lincoln threatened briefly, but Palmer survived a penalty appeal for a clumsy challenge on Stewart seconds later as the hosts responded.
Having introduced Joe Walsh and Conor McGrandles at the break, the visitors had a better shape and they were unfortunate not to reduce the deficit within six minutes of the restart when Regan Poole’s downward header reared up off the turf and hit the crossbar.
They got their reward in the 56th minute when Hopper climbed to head Jorge Grant’s corner firmly past goalkeeper Lee Burge and they passed up a glorious opportunity to make it 2-2 with 28 minutes to go after McGrandles had been tripped inside the box by Josh Scowen.
Grant sent the resulting penalty to Burge’s right, but the keeper guessed correctly to palm his effort away.
McGrandles could have killed off the tie with 10 minutes remaining only to fire high over after cutting inside substitute Max Power, but although McGeady hit the post and substitute Aiden O’Brien saw an 85th-minute shot saved, there was no way back for Sunderland.
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