The Gills have now gone five games without defeat, while Stanley have not won in eight and are falling further into the relegation mire.
They were just seven points clear of the drop zone before this clash.
Jackson gave the visitors the lead in the 18th minute when he poked home from close range for his 14th league goal of the season.
The 21-year-old had two other efforts either side of his goal.
John and Paul Mullin both had chances for the hosts, while James Ryan shot just wide.
Oli sealed the win for Gillingham with 23 minutes left when he latched onto Nicky Southall's ball to fire into the bottom right corner from 15 yards out.
The 25 year-old winger caused Accrington problems all afternoon and his third goal of the season was just reward.
Accrington had as many shots on target as the Gills, but their lack of confidence up front is proving a major issue.
Talismanic striker Paul Mullin has hit a lean patch just at the wrong time, while Craig Lindfield was below par and was substituted just before the killer strike from Oli.
Accrington have scored just three goals in their last eight games and are now five points above the drop zone.
The one frustration for manager Mark Stimson and his Gills was that promotion rivals Exeter and Bradford both won.