An own goal from TJ Eyoma put Posh 1-0 up after ten minutes before Anthony Scully equalised just after half-time.
Jorge Grant had a chance to win it from the penalty spot after a Nathan Thompson handball, but he put his effort wide. Both sides will be happy with a point as they continue their chase for promotion to the Championship.
Story of the match
Peterborough boss Darren Ferguson feared how the forced break would affect his players, but early on it was clear that it wasn't much.
Posh took an early lead after a period of sustained pressure in the opening ten minutes.
Nathan Thompson stole the ball off the inattentive Bridcutt and gave the ball to Clark-Harris, who hit the ball towards goal. The goal came in fortunate circumstances as an Adam Jackson block hit TJ Eyoma and bundled into the empty net.
The away side pressed high and looked very confident in possession. Lincoln were penned in for large swathes of the opening exchanges, with the game becoming physical as a result.
They could have doubled their lead when a Frankie Kent cross was met by Clark-Harris, but his header was weak and made for a comfortable save.
The referee brandished three yellow cards in the opening twenty minutes from fouls from Bridcutt, Jackson and Thompson.
Lincoln themselves were affected by COVID-19 in the week and it certainly showed in their performance. It took the Imps a while to settle before finally earning their first chance through Brennan Johnson.
Typically dangerous on the counter, Lincoln broke from a Peterborough corner as Johnson had half the pitch to run into alone.
He showed great pace but lacked composure in the box as he blazed his effort wildly over.
Michael Appleton will be disappointed his side didn't equalise ten minutes before half time when another quick transition led to a big chance.
Johnson and Grant played the ball quickly to unleash Remy Howarth in space on the right-hand side. Again the finish let down some good football for the hosts as Howarth's effort emulated Johnson's.
Just two minutes after half-time, Lincoln did get their equaliser. A Jorge Grant corner wasn't dealt with effectively from Peterborough, with Beevers ricocheting the ball. Scully was lingering around the back post and struck the ball into the top corner unmarked.
Peterborough, shocked after conceding so soon into the second half, looked to respond immediately. A set-piece routine of their own gave Clark-Harris a good opportunity to score his 13th of the season, but his header looped over and into the deserted stands.
In fact, it was the home side who sparked into life after the goal. They had a glorious chance to take the lead when Grant fizzed a low cross along the face of goal. Johnson met the ball at the front post and wheeled away in celebration as he struck it. Christie Pym had other ideas, pulling off an emphatic reactionary save to keep the scoreline level.
Lincoln enjoyed themselves down the right-hand side in the second half, exposing the defensive vulnerability of Harrison Burrows. Grant and Scully often overloaded the 18-year-old. After all their domination in the first half, Posh were now hanging on to keep the scores even.
On 65 minutes, the game was sent into chaos. Anthony Scully took a shot from 18 yards out but Nathan Thompson handled the ball in his block, giving Lincoln a penalty and also receiving a second yellow card for his troubles.
Jorge Grant stepped up to take the penalty but his effort was poor and went a yard wide of the right post.
A glorious chance went begging but the home side now had the one-man advantage for the final 25 minutes.
Pym was forced into action twice in quick succession as he saved efforts from both Johnson and Jones to keep his side in the game.
Ten minutes from time, Scully could have won it for Lincoln. The midfielder dummied a pass so the ball could travel to Eyoma out wide. His cross fizzed low into Scully but he couldn't find the touch to tap home from a few yards out.
The future of Siriki Dembele needs to be finalised as soon as possible. The forward rocked Peterborough this week by handing in a transfer request, however; he started the game on Saturday afternoon.
He looked disinterested for the most part and he was largely missing in action for Posh. On 70 minutes, he was dragged off for Dan Butler as Ferguson looked to change things after Thompson's sending off.
But his performance was that of a man who didn't want to be on the pitch. It is therefore essential for Peterborough to find a resolution to the problem as soon as possible. With five goals and four assists so far, Dembele has been a key player but, if he wants to leave, it may be beneficial for the team to let him go.