Almost 10,000 Black Cats fans returned to the Stadium of Light for this game after being locked out from seeing their team play live in the flesh for 15 months – and their players really rose to the occasion in the first half, with goals from Ross Stewart and a volley from Charlie Wyke cancelling out The Imps two-goal advantage from Wednesday night's first leg within the opening 45 minutes.
Burge did offer some hope to his side when he saved Jorge Grant's penalty on 63 minutes – but Lee Johnson's men could not find an equaliser, condemning them to a fourth successive season in the third tier.
Story of the game
Black Cats boss Lee Johnson – on the back of that first leg defeat – made a number of changes to his team, with Callum McFadzean, Grant Leadbitter, Chris Maguire and Ross Stewart all drafted into the side.
Michael Appleton made two changes from the midweek home victory, with Alex Palmer returning from injury to replace emergency goalkeeper Josef Bursik, as well as Lewis Montsma coming in to replace Adam Jackson.
The home side started the game well, buoyed by this raucous 10,000-strong crowd. They were full of energy, tenacious with their pressing – and it was not long before they drew first blood.
Sunderland took the lead – and pulled a crucial goal back in the tie – on 13 minutes when Aiden McGeady worked his way down the left-hand side, skinning Regan Poole before delivering a low-driven cross into the path of Stewart who expertly dispatched from close range.
The Black Cats had a half-chance to double their lead when a long-ball from the defence was chested down by Charlie Wyke into the path of Stewart, who this time sliced his shot wide of the goal.
The chances kept coming for Sunderland – and this should have been 2-0. The hosts pounced on some lackadaisical play at the back from Lincoln, freeing Wyke through on goal. The 30-goal striker skinned the goalkeeper, but took too long to find his finish, as Tj Eyoma raced onto the line to bloke the shot, before goalkeeper Palmer thumped the ball over-the-bar to safety.
As the crowd got louder, Sunderland got better – and on 33 minutes, they bagged their second of the game. McGeady was once again influential down the left-hand side as he found space to cross the ball into the path of Wyke, who this time made no mistake with his finish, volleying the ball with an outstretched boot beyond Palmer at full stretch.
Lincoln looked shot of confidence and completely shellshocked by the occasion – the polar opposite to how they were on Wednesday night.
They did have a few half-chances towards the end of the half through Tayo Edun and Jorge Grant, but none of them really troubled Lee Burge in the Sunderland goal – capping off the perfect first half from Johnson's men.
A Hopper header that turned the tie in Lincoln's favour
Lincoln started the second half a lot better than the previous 45 minutes – and had a great opportunity to retake the lead in the tie when Grant's corner was met by Poole, whose header crashed off the underside of the crossbar.
And just six minutes later after they hit the crossbar, The Imps retook the lead in the tie. A corner from the left-hand side was met beautifully by Tom Hopper who freed himself of his marker before heading past a helpless Burge.
Grant stepped up, but was denied by a top-drawer save from Burge that was met by an enormous roar by the Sunderland faithful.
It took until the 80-minute mark for another big chance to come calling – for the visitors again – as McGrandles skinned Max Power, freeing himself one-on-one with Burge, but skied his effort well over the crossbar.
Sunderland were desperate to keep their dreams of promotion alive – and they should have had a third goal when McGeady crashed the post with a side-footed effort before Wyke hit the rebound off the side-netting.
Another big opportunity came for the hosts on 85 minutes when substitute Aiden O'Brien used his pace to get through on goal and unleashed a strike at Palmer, who expertly blocked the shot at his near-post.
Lincoln had a big opportunity – just before we went into stoppage time – to all but secure their place at Wembley as Morgan Rogers caught Power napping down the left-hand side, but his curling effort was met by another crucial Burge save.
In added time, it was all about remaining resolute for the away side. They had every punch thrown at them by their opponents throughout the 90 minutes, but most importantly, they remained standing – ensuring they now are one win away from Championship football.
Lincoln will walk into Wembley with massive confidence
In 2017, Lincoln City were a non-league side, whilst Sunderland were a Premier League club.
Michael Appleton's side today moved one step closer to surpassing their opponents this afternoon, with a win that tested the metal of their squad to the absolute limit.
The 9,971 Sunderland fans made the Stadium of Light – for the first time in 15 months – a real cauldron of fire, and the players fed off it in the first half in particular.
The Black Cats erased Lincoln's two-goal deficit by half time, leaving their opponents completely shellshocked in the process – mainly by a crowd that felt, and sounded like 40,000.
But credit to Lincoln, they turned the tie back in their favour after the interval, when it seemed the odds were stacked against them.
They pressed higher up the field and quickly got their noses back in front. And by doing that, they seemed to expose a set of Sunderland players that almost looked burned out from a frantic, adrenaline filled first half.
That today, by far, was Lincoln's toughest test to date.
But by coming through that game, with them fans all against them, there cannot be a greater confidence booster than that; as The Imps head into one of the biggest games in their history next Sunday...
Sunderland: Burge; Gooch, Wright, O'Nien, McFadzean; Leadbitter, Scowen; Maguire, McGeady; Wyke, Stewart. (4-2-2-2)
Lincoln City: Palmer; Poole, Montsma, Eyoma, Edun; Johnson, Bridcutt, Grant; Scully, Hopper, Rogers. (4-3-3)