City put in a performance of true grit and desire, but were cruelly denied a point in their first game of the Championship season.
Adam Reach gave the Imps a deserved lead after 12 minutes, and the hosts were good value as they held that advantage at the interval.
But Will Lankshear struck twice in the second period - the second in time added on at the end of the match - to give last year's beaten play-off finalists the win.
Although there were no points to take back to Lincolnshire, Chris Cohen and Tom Shaw's side showed a level of commitment, application and no little skill to suggest they can be competitive in every game they play in the second tier.
The home side were the first to have a sight of goal as Luke Ayling flashed an effort wide after just two minutes, but City started brightly and forced a succession of corners.
City opened brightly and forced a succession of corners - with Adam Reach also seeing a shot blocked when a ball was cleared back into his path following Ivan Varfolomeev's free-kick.
The Imps did not look at all overawed by playing at the highest level they had for 65 years, and when they took the lead after 12 minutes it was fully deserved.
A long ball from goalkeeper George Wickens was headed on by Freddie Draper into the path of Tendayi Darikwa, whose low cross found the run of Reach who swept home.
City looked threatening for long periods in the first half, with Tom Hamer flashing a shot wide and Draper - who caused problems with his pace and power - delivering a cross from the left which just eluded Darikwa.
A Hamer throw also causes problems, with a Dom Jefferies effort blocked by Ayling and Draper also seeing ahot hit a home defender.
More than half an hour had elapsed by the time Wickens was seriously called into action to turn Will Lankshear's header wide from Alpha Kante's cross. Although Wickens was not to know it, referee Bobby Madley had halted play for Lankshear's push on Towler.
And, when the late pressure looked like breaking through, Towler was on hand with a key clearance from a left-wing cross after 40 minutes to preserve City's lead going into the break. There was also a big block from wickens to deny Kyle Joseph in time added on before the break.
There were no changes from either side at the interval, but the home side had clearly reset and Wickens was forced to palm away a Lankshear shot just two minutes into the second period.
The home side also went close through forme rImp Morgan Whittaker, whose free-kick went just over the bar.
But City's danger on the counter attack was highlighted moments later when Hamer outjumped Ayling to get on the end of a Jefferies cross from the right - his header went just over.
The Imps made a double change on the hour mark, with Rob Street and Tano Olaofe replacing Jefferies and Draper.
The equaliser came after 62 minutes. Ayling's initial cross from the right was headed away by Deji Elerewe, but a quick shot back into the area from Leo Castledine was deflected into the pass of Lankshear who fired home from close range.
There was a need for the Imps to dig deep, now, and Wickens got down well to block a low shot from Whittaker after 68 minutes. The forward also flashed a head wide after 75 minutes
City thought they had regained the lead after 82 minutes when a well-worked short throw from Hamer - after everyone had lined up for a long throw - ended up with Olaofe sending the ball into the net with a diving header. The assistant's flag was up for an offisde, though.
And moments later eh got another shot away - although one from an angle which was never going to trouble Radek Vitek in the home goal - after a smart counter attack.
City defended with real grit and determination and, although there were moments of real danger such as when Lankshear crashed an effort off the underside of the bar - they looked like holding on for a deserved point.
In the end, though, Riley McGree's low cross in time added on found Lankshear who turned the ball home at the near post.
Boro: Vitek, Brittain, Berhalter, Lankshear, Whittaker, Ayling, Castledine (Peart-Harris, 63), Joseph (Sarmiento, 71), Malanda, Borges, Kante (McGree, 63). Subs not used: Brynn, Jones, Arfsten, Edmunson, Ibeh, Cartwright.
Imps: Wickens, Darikwa, Reach, Towler, McGrandles, Jefferies (Olaofe, 59), House (Hackett, 70), Hamer, Varfolomeev, Elerewe, Draper (Street, 59). Subs: Gauci, Coubis, Bayliss, Melia, Elder, Honohan.
Referee: Bobby Madley
Attendance 31,487 (2,118 away)
