Paul Cook's side, League Two champions back in May, were two goals to the good at half-time and although Villa pulled one back shortly after the interval, the hosts made the game safe with a third late on.
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Substitute Jack Grealish brought the Premier League outfit back into the match in the 51st minute, but, as the visitors pressed for an equaliser, Sam Morsy restored Chesterfield's two-goal advantage six minutes from time.
Villa fielded a largely youthful starting XI as Paul Lambert looked to give his more inexperienced players some valuable game time.
But it was the hosts who started the brighter, going ahead after six minutes, as Darikwa got in behind the Villa defence and finished past Brad Guzan from a tight angle.
Guzan was forced into a save from Hird six minutes later, the American also keeping out a powerful header from Armand Gnanduillet.
Villa did have the ball in the net in the 28th minute, but Callum Robinson's header from Samir Carruthers' cross was disallowed for offside.
The visitors were showing signs of improvement, Graham Burke crashing a shot off the crossbar on the half-hour mark, but two minutes before the break Chesterfield doubled the lead when Hird slid in to convert a corner from Gary Roberts.
Villa made multiple changes at the interval, and they pulled themselves back into the match within six minutes, Grealish finishing coolly after good work by Leandro Bacuna and Charles N'Zogbia.
N'Zogbia - recovering from an Achilles problem that saw him miss the entire 2013-14 campaign - continued to look dangerous, beating two players and curling a shot off target in the 72nd minute, but the game was ended as a contest when Morsy broke clear to score late on.