Visitors Sawley eventually edged home by three wickets with nine balls to spare in the Division One clash.
Chesterfield were up against it for most of the match after sliding to 80-6 on winning the toss and batting.
The Sawley seamers bowled tightly in helpful conditions. Nottinghamshire opener Ben Slater played several fluent off-drives but was caught behind for 22.
In the following over Essex all-rounder Matt Critchley, making his seasonal debut for the club where he was a regular before establishing himself in the county game, was bowled for a first-ball duck by his fellow leg-spinner James Lawton.
The highly-promising Lawton (3-42) caused plenty of problems. Harry Wilmott tried to lift one delivery over the short leg-side boundary but swung himself off his feet and finished sitting on the ground beside his broken wicket as he too was bowled for 17.
The Chesterfield lower order then launched a fightback. Wicket-keeper David Hunt (20) and Saad Sarwary (18) gave valuable support to Alex Fowkes, whose 52 not out steered the hosts to 202-9 off their 50 overs.
This included an unbroken last-wicket of stand of 43 with captain Alex Hibbert (17 not out), who normally bats in the top order but, suffering from a neck injury, held himself back to No.11.
Sawley were in control for most of the second innings. Critchley (3-48) took two wickets in successive overs to make them 101-4 and the game was in the balance when left-arm spinner Yannick Leonard and paceman Sarwary reduced them to 150-6.
But Jacob Taylor smashed four sixes in a rapid 36 not out to settle the issue.
Meanwhile, a second-wicket stand of 208 steered Chesterfield Seconds to a six-wicket win at Marehay in Division Three North.
The home side raced to 280-4 off 45 overs but Sam Fawcett (136 not out) and skipper Corey Green (70) made light of the task as Chesterfield powered home with ten balls in hand.
Chesterfield thirds lost by 210 runs after being bowled out for 84 by Eckington in Division Nine North.