Lincoln overcame a potential FA Cup banana skin at Chesham with a 4-0 victory at The Meadow.
Goals by Jack Moylan, Jovon Makama, Conor McGrandles and an own goal from Callum Adebiyi set up an all-Sky Bet League One clash with Crawley in the second round.
Chesham came close after 38 minutes when goalkeeper George Wickens had to claw away a looping Nathan Minhas header after a Samson Esan cross.
However, Lincoln took the lead two minutes before the break when Moylan showed good control in the area to curl his effort past the outstretched Ben Goode.
They effectively secured their passage into the next round three minutes after the interval when Makama broke the offside trap to coolly slot home his effort.
McGrandles made sure of the win after 65 minutes when his shot from the edge of the box took a massive deflection past the grounded Goode.
The Chesham keeper pulled off a spectacular save from JJ McKiernan by turning his 76th minute shot on to the crossbar.
The fourth Lincoln goal saw Goode try to clear from Lincoln’s Zane Okoro, but saw his attempted clearance with four minutes remaining deflect off the hapless Adebiyi and into the net.