City, missing five first-choice players, started nervously but once in front they were the only team likely to win.
County, the League Two draw specialists, created few chances and rarely tested Lincoln's rookie keeper Simon Rayner.
Stockport created an opening after only seven minutes when Matthew Hamshaw beat three defenders but failed to hit the target with his final shot.
Lincoln's Gary Birch had a goal disallowed for pushing but County had the better of the opening 45 minutes.
They went close when Hamshaw struck a superb 25-yard free-kick only to see Rayner bring off a diving save.
Then Hamshaw's 45th-minute corner created a chance for Chris Williams but the midfielder headed over from six yards.
Lincoln looked a different team after the break and almost went in front within seconds of the restart.
Steve Robinson, back after a two month injury lay-off, sent Dean Keates clear but the midfielder's left foot shot flew wide.
Scott Kerr had a shot saved by keeper Carl Ikeme and then Lincoln's Gareth McAuley had a far post header blocked on the line by Keith Briggs.
Lincoln finally got on the score sheet in the 52nd minute when striker Gary Birch was allowed to run through from midfield before netting with a low drive into the bottom corner.
Birch put another effort inches over the bar before going on to grab his seventh goal of the season with 13 minutes left.
Derek Asamoah beat his man down the flank before sending over a neat cross which Birch struck first time into the net.
Lincoln almost added a third goal seconds later when substitute Luke Foster won the ball in midfield but smashed his final shot inches wide of the post.