Peter Clarke and substitute Billy Mckay pulled two goals back with 20 minutes to play and despite a host of chances, Athletic were unable to convert them and go out of the Emirates FA Cup.
Two early first half goals from Theo Robinson and Terry Hawkridge put the Imps ahead at the break whilst a minute after the restart, Robinson grabbed his second of the game and Lincoln’s third.
Latics fought back but the late goals were not enough and Athletic exited the competition.
Manager Stephen Robinson made five changes from the side which drew 2-2 with Port Vale two weeks ago.
One of those players, Cameron Dummigan, earned an early booking for a late challenge on Alan Power.
Lincoln City could have been awarded a penalty only a minute later as Jamie Reckord appeared to handle the ball in the penalty area but the referee was unmoved.
Latics did have the first chance of the game on six minutes as Freddie Ladapo turned inside the area but goalkeeper Paul Farman made the save.
Dummigan was forced to clear in front of his own six yard box on 13 minutes whilst two minutes later, Hawkridge forced a good save from Connor Ripley after being released in the penalty area.
Latics had the perfect opportunity to take the lead seconds later. Ollie Banks’ ball found Lee Erwin and he picked out the onrushing Ladapo but he knocked it past Farman’s post.
Athletic were made to pay for that missed chance as Lincoln took the lead midway through the first half.
Matt Rhead headed into the path of the onrushing Robinson who made no mistake from inside the six yard box to put the National League side the lead.
Two minutes later and the home side extended their lead through Hawkridge.
The winger intercepted a poor pass from Carl Winchester and he confidently slotted past Ripley to extend Lincoln City’s lead.
Robinson almost made it three to Lincoln on the half hour mark but his close range shot went over the crossbar.
Latics needed a response and almost pulled a goal back as Ryan McLaughlin crossed low for Ladapo but he was crowded out in the penalty area.
Banks and McLaughlin both went close soon after whilst Winchester almost made amends for his earlier error but shot inches wide from 25 yards.
The hosts almost made it three on the stroke of half time but Robinson struck wide from inside the penalty area after being set free in the penalty area.
Athletic had an early opportunity in the second half as Green volleyed wide from 25 yards but were made to pay for that miss a minute later as Lincoln made it three.
Robinson capitalised on a loose ball and lifted the ball over Ripley to make it three for the hosts.
Latics almost got an instant response as Winchester fired wide from 25 yards but two minutes later he was substituted in place of Lee Croft.
Just after the hour mark, Erwin curled towards the top corner but Farman in the Lincoln goal was equal to the effort and tipped it over the crossbar.
Mckay entered the action on 66 minutes and added some pace to the attack.
On 70 minute, the captain Peter Clarke led by example and gave Latics a glimmer of hope, heading home at the bad post to pull a goal back
Three minutes later and Athletic were back in the game as substitute Mckay made it 3-2.
Erwin flicked the ball into the path of the Wigan Athletic loanee and he lifted the ball over the goalkeeper and into the far corner.
The momentum was with Oldham Athletic as Croft struck goalwards from 25 yards which the goalkeeper was forced to save and from the resulting corner, Ladapo headed over from six yards.
Athletic continued to press for the leveller as Banks’ corner found the head of Cameron Burgess but from six yards, the defender headed wide.
Latics fought until the end as Banks went close and in the final minute Ripley went up for a corner which bobbled around the box but the referee blew the final whistle and Latics exited the competition.
Lincoln City: Farman, Wood, Habersham, Waterfall, Power, Rhead, Hawkridge (Anderson 72’), McCombe, Arnold, Woodyard, Robinson (Muldoon 80’).
Subs not used: Marriott, Fixter, McMenemy, Weatherall, Walton.
Oldham Athletic: Ripley, Dummigan, Clarke, Burgess, Reckord (Mckay 66’), Winchester (Croft 55’), Green, Banks, McLaughlin, Erwin, Ladapo (Osei 77’).
Subs not used: Kettings, Law, Dunne, Fane.
Goals: Lincoln City (Robinson 22’, 47’ Hawkridge 24’) 3-2 Oldham Athletic (Clarke 70’, Mckay 73’)
Attendance: 7,012 (415 visiting supporters)