Anthony Scully was on hand to notch The Imps in front courtesy of a rebound midway through the second half - cancelled out by Charlie Wyke's towering header - his fifth goal in two games, which sent the game to penalties.
Lincoln's Remy Howarth smacked the crossbar with The Imps' third penalty of the shootout - setting up veteran midfielder Grant Leadbitter to cooly place his spot-kick into the bottom-right corner of the net to seal Lee Johnson's side a place at Wembley Stadium to face League Two outfit Tranmere Rovers next month.
Story of the game
The first half-chance of a cagey opening 45 minutes came from the visitors just north of the ten-minute mark when Jorge Grant's corner provided a free header for Lewis Montsma, but the chance came and went for the defender as he headed well over the Sunderland bar.
Lincoln dominated possession in the early exchanges and looked to carve The Black Cats open with some smart, quick-passing play between Anthony Scully and TJ Eyoma. Eyoma found some room to shoot on the edge of the penalty area, but skied his effort well over the crossbar.
Some lackadaisical play in the middle of the park from Aiden McGeady seen Lincoln pounce with pace. Brennan Johnson picked out Scully, but he had a similar fate to his teammate Eyoma earlier - with his shot going his and wide of Lee Burge's goal.
After the 25 minute mark, Sunderland came into their own and arguably had the best chance of the game when McGeady worked some space to play the ball to an overlapping Callum McFadzean - but his deflected effort went inches past the post.
McGeady was the architect again on 37 minutes - his cross towards the in-form Charlie Wyke was headed away by Lincoln, but only as far as Grant Leadbitter, who shanked his effort well clear of The Imps' goal.
The star man of a tetchy first half McGeady was the focal point for any Sunderland attack, and this time he used his skill to work himself into a shooting position, but his effort was met by a good save by Alex Palmer in the Lincoln goal.
A second-half that provided some much-needed entertainment value
Bailey Wright was forced off for Conor McLaughlin at the break, meaning Sunderland had no registered central defenders on the pitch in the second half. Lincoln almost took immediate advantage of that 20 seconds after the restart when Tom Hopper broke on the counter and forced a solid save out of Burge.
This semi-final needed something to bring it into life, and that came through Grant's glaring miss for Lincoln when he shanked his effort from the middle of the goal well wide of the Sunderland goal.
Spurred on by Grant's earlier miss, The Imps took the lead on Wearside in the 64th minute when Conor McGrandles' initial shot was saved by Burge, but left Scully unmarked to fire the rebound into the bottom-right corner.
Lincoln attempted to protect their lead heading into the final 20 minutes of the game, and a flurry of Sunderland chances appeared. Lynden Gooch with a notable strike hit from distance, but it was saved comfortably by Palmer.
Max Power found some room down the right-hand side and played an inch-perfect cross towards an unmarked Wyke, six-yards out from goal, but his header bounced into the ground and was easily tipped over the crossbar by The Imps goalkeeper.
Wyke's perseverance in front of the goal paid off on 75 minutes, and it was that duo again: himself and McGeady that grabbed the equaliser. Sunderland's top scorer got the run on his marker and headed the ball into the bottom corner of the net to level the game up.
Sunderland pushed for an equaliser, McGeady again a nuisance, found some room from 25-yards to rifle a shot at goal, but his effort was matched by a good stop by Palmer.
The Black Cats' pressure in the final few minutes came to no prevail, but five perfect penalties from Power, Luke O’Nien, Chris Maguire, McGeady and then Leadbitter to set up another trip to Wembley for Sunderland.
Lincoln's attempt to sit on their one-goal advantage cost them the game
When Anthony Scully wheeled away in celebration on 64 minutes, it almost looked like The Imps had one foot inside Wembley Stadium.
They were a goal in front - playing against a Sunderland side with natural centre-backs on the pitch, and were seemingly in full control of the game with just 25 minutes to go.
Then, their system seemed to dramatically change once they grabbed their goal. They sat back to protect their lead against a Sunderland side full of goals, and ultimately full of confidence after they dismantled Doncaster Rovers on this very turf last weekend.
The decision to defend deep backfired for Michael Appleton's side, who were subsequently thrown into the lottery of a penalty shootout, despite being in a commanding position to potentially go on and kill the tie off.
Sunderland, however, must be given huge credit for this victory. Not only did they banish their penalty demons from their 2019 final defeat to Portsmouth in this exact competition, but they equally matched the top side in their division with a makeshift defence.
The Black Cats will now descend on the capital in less than a months time - knowing they are huge favourites to seal a Wembley win for the first time since their historic FA Cup triumph in 1973.
Sunderland: Burge; Power, Wright, O'Nien, McFadzean; Scowen, Leadbitter, Neill; McGeady, Wyke, Gooch. (4-3-3)
Lincoln City: Palmer; Eyoma, Montsma, Jackson, Edun; Sanders, Grant, McGrandles; Johnson, Hopper, Scully. (4-3-3)