Spireites scored first but then conceded three to lose to a strong Hull City side.
Ian Evatt and Harry Maguire each headed first half goals before the East Yorshire visitors went on to control the game after the break with goals from Andy Robertson and sub Calaum Jahraldo-Martin, who converted after Uruguayan Abel Hernandez had caused havoc in the home defence.
Spireites’ first home line-up under new manager Dean Saunders saw him adapt a 4-4-2 formation and it soon became clear that he wants his team to play the ball to feet whenever possible but get it forwards quickly.
Full backs Darikwa and Dan Jones were clearly vital in that aim with the former looking in majestic form.
Supporters had been boosted by the news that goalkeeper Tommy Lee has pledged his future to the club, the new deal, set to be signed, is believed to be for three more seasons.
Hull City selected a starting eleven that cost a princely £22.5 in transfer fees - though £6.5m man Nikica Jelavic looked isolated at times with Sone Aluko frequently appearing the most likely danger man.
Sylvan Ebanks-Blake forced the first save with a rising angled drive whilst former Sheffield United man Maguire, playing on front of the trio of central defenders, had a shot blocked and he hit a volley too high.
Darikwa was instrumental in the opening goal; his driving run almost forced an own goal, Allan McGregor had to tip a rebound from the full-back’s cross over and the short corner routine saw Darikwa pick out Evatt to head home, unmarked, from eight yards.
Both sides looked capable of scoring, Sam Hird for the hosts and Aluko came close before former Blade Maguire leveled with a close range header from another short corner routine.
Sam Clucas drove close from 25 yards as half-time approached in what had been an even contest.
Hull started the second half strongly with Matty Dixon forcing a low save from Lee before Robertson drive in a fine angled left footer to give City a lead they never looked like relinquishing.
John Meyler, who later on was subbed after an altercation with Sam Morsy, went close as did the powerful Dame N’Doye before Jahraldo-Martin scored from the box-edge after Hernandez had drawn Lee and Jones into challenges that led to the loose ball falling kindly for the Antiguan.
Spireites rarely troubled second half keeper Eldin Jakupovic but their first half show had plenty of encouragement for Saunders who now awaits Sean Dyche’s Burnley who visit the Proact on Saturday.
Chesterfield’s performance may have fizzled out, but the club were optimistic.
They tweeted: “Very Good Spireites start, but higher division quality from the Tigers saw them dominate the second period and claim their win.”
Dean Saunders confirmed all of his players came through the game unscathed whilst Tommy Lee indicated his groin injury had completely healed and his fitness level was 100 per cent.
Drew Talbot could come into contension for the weekend.
Chesterfield: Lee, Darikwa, Hird (Orrell 74), Evatt, Jones (Harrison 89), Morsy, Gardner (Ariyibi 68), Banks (Donohoe 78), O’Shea (Raglan 58), Clucas, Ebanks-Blake (Gnanduillet 68).
Hull: McGregor (Jakupovic HT), Maguire, Bruce (Dixon HT), Dawson, Davies (Chester HT), Brady (Jahraldo-Martin 66), Robertson (Townsend 80), Elmohamady (Lenihan 78), Meyler (Clark 80), Aluko (Hernandez 74), Jelavic (N’Doye 61).
Goals: Maguire 37, Robertson 51, Jahraldo-Martin 75