Roberts struck in the 33rd minute after sustained pressure on Ryan Clarke's goal before Jagielka doubled the home side's advantage with a superb volley.
Clarke had no chance as the ball flew into the top corner and Accrington had almost sealed the points.
The home side should have won by more, but manager John Coleman was happy with the points as they continue their charge up the table.
It was Accrington who came out of the traps flying and in the fifth minute David Brown saw a shot charged down.
At the other end Zema Abbey saw a powerful header fly inches wide as Forest Green nearly scored against the run of play.
But that near miss only served to inspire the home as they peppered the Forest Green goal.
Ian Craney fired wide in the 16th minute and two minutes later the impressive Paul Mullin missed the target with a fierce drive.
Mullin saw a shot saved by Clarke in the 22nd minute as Accrington looked for the opener and eventually the pressure told.
Roberts drilled a powerful left-footed shot into the corner and there was nothing Clarke could do about it.
Then it was Jagielka's turn to get on the scoresheet with his wonderful volley.
With the Forest Green defence closing him down, the midfielder hit the ball sweetly into the top corner.
The visitors nearly hit back on the hour-mark through Abdou Sall but he fired over the bar when he should have done better.
Anthony Barry had a shot blocked in the 65th minute as Accrington looked to make it a hat-trick of goals, while Roberts came close to grabbing his second of the game only to see a shot saved by Clarke.
Craney shot wide near the end while Guy Madjo had a good chances for Forest Green.
But Accrington deservedly took the points and were much the better of the two sides.