The veteran full-back’s 25-yard thunderbolt in first-half injury-time was a rare moment of quality in a dour affair at Sincil Bank.
City striker Matt Green should have scored inside the first minute, but he only toe-poked the ball goal-wards a yard out after a scramble in the box and his effort was blocked.
Mo Eisa brought an excellent low save out of Lincoln goalkeeper Ryan Allsop after quarter of an hour, before visiting stopper Scott Flinders tipped Green’s excellent header over the crossbar just before the break.
Eardley then let fly in stoppage-time from distance, sending a screamer past Flinders and securing the Imps a half-time advantage.
Ollie Palmer came off the bench after an hour and almost made an immediate impact, heading Eardley’s cross inches over.
Another Palmer header was kept out by Flinders, before the big frontman hooked an effort over.
It was not all one-way traffic as Allsop came to City’s rescue to brilliantly deny Robins substitute Sanmi Odelusi, before the on-loan keeper saved from the Robins’ leading scorer Eisa.
Green was put through by Palmer in the last minute but Flinders rushed out to block his strike on goal, before Harry Anderson also saw a late shot saved.
Uwe Rosler was sacked by Fleetwood following a 3-0 reverse at Doncaster which condemned Town to a seventh straight defeat in all competitions.
Cambridge interim head coach Joe Dunne was pleased with how his side adapted to beat Grimsby 3-1.