It was job done as strikes from Jack Moylan, Jovon Makama and Conor McGrandles, in addition to an own goal, secured City a place in the second round of the Emirates FA Cup.
It was a professional performance from the Imps, who will head to Crawley in the second round of the famous competition.
Head coach Michael Skubala made five changes from the side that beat Northampton Town last time out, with the Academy graduate pairing of Jovon Makama and Freddie Draper reunited up front.
It was a tight opening spell at The Meadow, with Makama registering the first chance of the match with an effort after six minutes which was deflected behind for a corner.
The home side threatened with a header from a corner after 13 minutes, but from that point City started to show their quality.
A Moylan run after 23 minutes was stopped by an excellent tackle from Connor Stevens, while the midfielder was again the danger two minutes later when he tried a shot from danger - though there was no real risk to Ben Goode in the home goal.
The Imps had a run of corners before Moylan again tried his luck from distance - this time he was just inside the opposition half when the ball broke nicely for him. Goode collected at the second attempt.
Draper, on the stretch, could not keep his header down from a Roughan cross while a great interception was needed to flick the ball off Erik Ring’s head from a Reeco Hackett cross.
Wickens was called into his first save of note after 38 minutes to stop Nathan Minhas’ smart header from a Samson Esan cross.
City had the best of the latter stages of the half, and it was little surprise that when the deadlock was broken it was by Moylan.
T’Sharne Gallimore headed away Draper’s effort, but it was only cleared as far as the Irishman who cut inside before curling home a right-footed finish into the far corner.
That goal pierced the confidence of the home side, and Makama deflated them completely when he struck early in the second half.
A smart flick by Draper sent him through, and he calmly finished low past Goode to make it 2-0.
City were now in control of the match, with a great interception turning a Roughan cross behind and Makama again going close.
A run of corners led to City’s third goal after 65 minutes. Moylan’s set-piece was only partially cleared, with McGrandles collecting the ball and making space for himself to fire home a low effort - with a deflection which wrong-footed Goode.
Skubala made his first changes after 69 minutes, sending on Ethan Hamilton and Bailey Cadamarteri in place of goalscorers McGrandles and Makama. Dom Jefferies joined them five minutes later, replacing Hackett.
City were in game management mode, now, but had opportunities to add gloss to the result.
It took an acrobatic flying save from Goode to deny JJ McKiernan after 76 minutes. A series of blocked shots on the edge of the area came before Moylan played through McKiernan, who tried to poke the ball home - Goode’s effort tipped the ball onto the bar.
There were further late changes for the Imps, with Academy graduate Zane Okoro sent on for his debut and Saxon Earley also coming off the bench.
Okoro was heavily involved in the fourth goal, having been sent through by Cadamarteri. Okoro couldn't get his feet sorted out, but Goode's clearance bounced off Callum Adebiyi and ended up in the back of the net.
Chesham: Ben Goode, Lewis Rolfe, Alex Lafleur, Jack Cawley, Connor Stevens, Callum Adebiyi (c), T’Sharne Gallimore, Ashley Lodge, Samson Esam, Nathan Minhas, Mitchell Weiss. Subs not used: Oliver Steinke, Steve Brown, Bradley Clayton, Jack Connors, Joe Grant, Ryan Upward, Connor Roberts, Avan Jones, Omar Rowe.
Imps: George Wickens, Eirk Ring, Tendayi Darikwa, Paudie O’Connor (c), Sean Roughan, Reeco Hackett (Dom Jefferies, 76), Conor McGrandles (Ethan Hamilton, 69), Jack Moylan (Saxon Earley, 80), JJ McKiernan, Freddie Draper (Zane Okoro, 80), Jovon Makama (Bailey Cadamarteri,, 69). Subs not used: Jamie Pardington, Ben House, Denny Oliver, Charlie Parks.
Referee: Alex Chilowicz.
Attendance: 3,963 (364 away).
