Darikwa's 46th-minute strike sealed a fifth league victory and gave Chesterfield their best-ever start to a season in 114 years.
Chesterfield dominated from the start although Danny Webber forced a good save from Tommy Lee in a rare Accrington break before Danny Winnard made a great block to deny Gary Roberts in the 18th minute.
Sam Hird missed a great chance to celebrate his 22nd birthday with a goal when he shot wide from 10 yards and Marc Richards wasted another opening for Chesterfield in the 36th minute when he shot over from 12 yards.
But Accrington fell behind 52 seconds after the break when Richards thumped a shot against a post and Darikwa fired the rebound past Marcus Bettinelli from 15 yards.
A goal-line clearance by Robert Atkinson denied Drew Talbot a second in the 63rd minute and Chesterfield survived some anxious moments in the closing minutes before Eoin Doyle hit the crossbar in time added on for the home side.