The Shots almost sneaked in front after only 15 minutes when Kirk Hudson put Scott Donnelly clear but the midfielder was denied by the woodwork.
Two minutes later Lee Beevers set up a chance for Geoff Horsfield but the veteran's downward header was saved by Mikhael Jaimez-Ruiz.
Horsfield then had another great chance when the ball rebounded off Ben Wright to send him clear but his shot was again saved by the 'keeper.
With the Aldershot defence all at sea Wright then flicked the ball on for Horsfield but Jaimez-Ruiz made another excellent save.
Lincoln paid the penalty for failing to take their chances when Aldershot snatched the lead in the 26th minute. Louis Soares played the ball in for John Grant to find the net with an excellent glancing header.
Five minutes later Lincoln's defence opened up again but 'keeper Rob Burch got down well to keep out an effort from Soares.
Burch saved again from Jake Robinson but Lincoln wasted another simple chance in first-half stoppage time.
Beevers went down the left and sent in a dangerous cross but both Wright and Horsfield failed to connect.
Horsfield was replaced by Sam Mullarkey at the break with the sub adding some life to the home attack. But Wright missed two more chances and Aldershot always looked the more likely team to score.
Hudson found Scott Davies with a pass but the midfielder curled his effort just over. The Lincoln defence opened up again three minutes from time when Grant burst through but hit his shot against the bar.
The inevitable second goal for the Shots did come though just two minutes from the end.
Davies, playing the final game of his loan spell, picked his spot from 25 yards to mark his final appearance for the Shots with a wonder goal.