Gillingham edged past League 2 Stevenage courtesy of Luke Norris’ first half penalty.
Norris put the Gills ahead from the penalty spot after Cody McDonald was taken down in the box.
Gavin Hoyte was sent off for the Gills in the second half but the visitors did enough to book their place in round two.
Gills boss Peter Taylor made six changes to the team which started Saturday’s match against Crewe, for the Johnstone’s Paint Trophy first round match.
Callum Davies captained the side as he made his third start of the season.
Those missing included leading scorer Danny Kedwell, central defenders John Egan and Kortney Hause and man-of-the-match from the Crewe game Jermaine McGlashan.
There were two familiar faces in the Stevenage starting XI as former Gills players Charlie Lee and Chris Whelpdale both faced their old team.
It was Lee who had the opening chance of the match, shrugging off the challenge from Jake Hessenthaler before forcing a save from keeper Glenn Morris.
But the Gills were ahead after 16 minutes when keeper Chris Day brought McDonald down in the box. The Gills striker was chasing a great ball forward from Bradley Dack.
Referee Darren Deadman issued Day with a yellow card, when it could easily have been red. But from the spot Norris converted to put the visitors ahead and claim his first goal for the Gills.
Stevenage ended the half putting plenty of pressure on the Gills goal but a couple of Lee efforts that went wide were as close as they got to levelling before the break.
Taylor took McDonald and Joe Martin off at the break, replacing them for Antonio German and Devante McKain.
Gills had a great early chance to make it 2-0. Dickenson had a shot saved by Day and his follow-up cross was headed over by Norris.
Norris had another chance on the hour, after wriggling free of the defence, but Day saved with his legs. German fired the loose ball well wide.
The Gills were down to 10 men when Hoyte was sent off for a challenge on Roarie Deacon. Referee Deadman issued a straight red for the foul.
Morris saved well from Deacon on 72 minutes after the hosts broke, attacking with three men against two Gills defenders.
The Gills keeper – replacing Stephen Bywater between the sticks for the night – was then forced to make a double save, to first deny Cameron Lancaster, before getting behind Calcutt’s follow-up.
Desperate penalty appeals from the home side came in stoppage time as Lee went down easily in the box. The referee said goal-kick.
Late chances from Charles and Calvin Zola went wide as the Gills hung on.
Gillingham: Morris, Hoyte, Martin (McKain 46mins), Legge, Davies, Hessenthaler, Pritchard, Dack, Dickenson, Norris, McDonald (German 46mins). Subs not used: Millbank, Fish, Hadler.
Stevenage: Day, Whelpdale, Walton, Charles, Calcutt (Marriott 80mins), Wells, Lee, Okimo, Lancaster, Henry (Ashton 87mins), Deacon (Zola 80mins). Subs not used: Beasant, Casey.