City’s veteran striker Geoff Horsfield missed a hat-trick of chances in the first 20 minutes – and Lincoln were made to pay for their poor finishing when John Grant headed the shots in front in the 26th minute.
Louis Soares almost added a second goal five minutes later when he burst in to the box but smashed his shot against the post.
Lincoln had a great chance to level in first-half stoppage time when Lee Beevers found Horsfield in front of goal but the striker failed to connect from five yards.
Horsfield was replaced during the break but Lincoln still struggled to threaten the visitors, although Ben Wright was denied by a double save from Shots keeper Mikhael Jaimez-Ruiz. But Aldershot finished the stronger and Scott Davies fired narrowly over after being put clear by Kirk Hudson.
Grant then smashed a shot against the bar before Aldershot added a second goal two minutes from time when Davies collected the ball 25 yards out and fired a shot straight in to the top corner, giving Lincoln keeper Rob Burch no chance.