Town striker David Ball’s cross was parried by Gills goalkeeper Glenn Morris and Evans reacted fastest to slot home the 18th-minute winner.
Evans was involved in another Town chance five minutes later but Ball fired narrowly wide at the end of a free-flowing move.
Ball was denied in the 56th minute by a spectacular Morris save, before Gills defender Max Ehmer diverted his shot narrowly past the post seconds later.
The Gills, who are now without a home win in four games , came closest when Luke Norris’ low shot was deflected just wide by Steven Schumacher.
Winger Jermaine McGlashan fired at Town goalkeeper Chris Maxwell following a quick break, and John Egan headed straight at Maxwell from five yards after he had only partially cleared Doug Loft’s corner.