The striker opened the scoring from the penalty spot on 21 minutes after Dion Pereira had been tripped on the byline.
Jerome then doubled the advantage eight minutes later, when Carlos Mendes Gomes’ pressing won the ball in Gillingham’s third and put Harry Cornick into the box.
Cornick returned it to Mendes Gomes, who helped it onto Luke Berry to tee up Jerome for a side-footed finish into the bottom corner.
Gillingham had threatened early and again soon after the second goal, but keeper Matt Macey saw the first shot fly over the bar and comfortable held the second with a routine save.
Manager Nathan Jones made three changes at half-time, bringing on Jordan Clark for Henri Lansbury, Luke Freeman for Berry and Cauley Woodrow for Cornick.
Gillingham halved the deficit with a header from a corner five minutes into the second half, then the Jones changed the rest of the team on the hour before former Town midfielder Olly Lee – scorer of the goal that sealed our promotion from League Two four years ago – whistled a 25 yarder just past Harry Isted’s right post.
Gabe Osho went close to adding a third with a header from a Freeman cross in the closing stages, but the final whistle blew on another 2-1 win to follow-up the victory by the same scoreline over NK Bravo in Slovenia last Friday.
Town: Macey (Isted 60), Onyedinma (Bree 60), Lockyer (Burke 60), Bradley (Osho 60), Bell (Potts 60), Pereira (Doughty 60), Mendes Gomes (Muskwe 30), Lansbury (Clark 45), Berry (Freeman 45), Cornick (Woodrow 45), Jerome (Adebayo 60).
Goals: Jerome 21, 29