Lewis Montsma's second goal of the season earned the Imps a deserved point after an impressive battling performance at Hillsborough.
The visitors created the best chances in the opening half - enjoying almost 60% of possession - but could not find a way through.
Dennis Adeniran's goal early in the second period gave the Owls some impetus and something to hold onto, but when Montsma headed home from a corner with 10 minutes to go it set up a finish where the visitors looked most likely to snatch a winner.
In the end neither side could find another breakthrough, and Michael Appleton's men could return to Lincolnshire able to reflect on a resolute away display and well-earned point.
Adam Jackson replaced the injured Joe Walsh at centre-back while Regan Poole returned to the starting line-up in the right-back slot after missing the midweek game against AFC Wimbledon, with keeper Archie Mair and forward Freddie Draper coming onto the bench after recovering from injuries.
The Imps settled in quickly, with Lewis Fiorini registering the first chance of the game after collecting a short free-kick from Chris Maguire. His long-range effort was deflected by the remnants of the Owls' defensive wall.
Anthony Scully was gifted an opportunity for his 12th goal of the season after a combination of hesitancy at the back from the home side an a high press from the Imps saw Maguire dispossess centre-back Dominic Iorfa and send the Irish forward through on goal.
Scully was left with an acute angle, with Bailey Peacock-Farrell getting down well to save with his legs. This was the start of a pattern throughout the opening half, where the visitors' best opportunities came from winning the ball back in the final third.
The home side looked dangerous in spurts with there absolutely no doubt about the quality of players on show in their expensively-assembled side. Conor McGrandles blocked a Barry Bannon shot, while Adam Jackson had to be alert to nick the ball off the toes of Lee Gregory.
Griffiths had to come out quickly to smother the ball ahead of Gregory, the Owls' centre-forward, after he'd played a smart one-two with Saido Berahino.
Scully had his second good chance of the game on the half-hour mark after Ted Bishop got away from Iorfa and played a defence-splitting pass. Scully did not manage to get his shot away and went down under pressure from Marvin Johnson and Liam Palmer although the referee felt there was no foul.
The next opportunity also fell the way of Scully, after the referee played advantage when Fiorini was felled while leading a counter-attack move. The ball was fed through to Scully, whose shot from distance was too close to the keeper.
Both sides enjoyed opportunities as the opening half drew to a close, with Griffiths saving well with his legs after Berahino got away from Poole to get a shot in.
And Maguire took advantage of a wayward backpass to collect the ball, he fed Fiorini but his effort was too close to Peacock-Farrell.
The nervousness of the home side remained there in the early period of the second period, with a ball into the area from Sorensen not remotely dealt with by Iorfa.
Maguire was able to keep the ball in the area, as well as stab it across the goal-line past Peacock-Farrell. But, with Scully looking to pounce, Jack Hunt was on hand to clear the ball.
Jamie Robson was also allowed the freedom of Hillsborough to waltz into the area, laying the ball off to Fiorini but the midfielder's effort was a good height for Peacock-Farrell to turn the ball away.
When the home side went ahead after 55 minutes it was against the run of play, with Fisayo Dele-Bashiru able to cut inside and fire a powerful shot from outside the area. Griffiths did well to get down and palm it away, but Denis Adeniran was first to react and finished from a tight angle.
Goals change games, and with the home crowd now getting behind them the Owls enjoyed their best spell of pressure of the encounter. The Imps dug in, though, and although they conceded several corners were able to protect Griffiths from needing to make any more saves.
Dele-Bashiru fired wide after barging his way into the area, while Iorfa lifted an effort over after finding himself in the area.
Draper, who signed his first professional deal at the start of this season on his 17th birthday, came on for the final 20 minutes for his senior debut in place of Scully.
Dan Nlundulu was also sent on, replacing McGrandles, but when the equaliser came it was not from either of the attacking additions but centre-back Montsma.
A corner was well won by Poole, and Montsma got away from his marker to get on the end of Maguire's delivery. His run toward the near post was enough to shake off Iorfa, and the ball went low from his flicked header and past Bailey-Farrell.
The belief and momentum was all back with the Imps now, with Bailey-Farrell having to be out confidently to collect the ball under pressure from Draper and Nlundulu after Poole headed the ball into the are from a deep Maguire free-kick.
And Draper just could not spin away from his man after collecting a pass from Bishop with five minutes to go.
Callum Paterson headed just wide for the home side from a corner in the 87th minute, but despite some nervy moments in the closing stages the Imps were able to leave with a good point.
Attendance: 23,521 (3,170 away tickets sold)