It was their greatest margin of victory by runs since they joined the Derbyshire League in 1999.
The top four batters in the Chesterfield order all played significant innings in the Division One clash before paceman Saad Sarwary scuppered the home side's reply.
Yannick Leonard (39) and skipper Harry Wilmott got Chesterfield off to a flying start with a stand of 117. They hit boundaries in 13 of the 15 overs they were together.
Wilmott piled on the agony for the bottom-of-the-table side's bowlers as he powered to 89 off 80 balls.
Alex Hibbert (63) and Luke Westwell (78 not out) maintained the tempo as Chesterfield posted a massive 343-5 off 50 overs. That equalled the first team's third highest total in the League.
Sarwary, bowling a full length and straight, made sure Elvaston did not get near it.With the first ball of the innings he had Andrew Wells edging a catch to wicket-keeper David Hunt.
He followed up by bowling two batters with successive deliveries in his third over and claiming an lbw victim in his fourth. His spell of 4-29 reduced the hosts to 53-5.
Leonard and Tom Keenan claimed two wickets apiece as Chesterfield wrapped up victory in the 28th over with Elvaston dismissed for 101.
The victory lifts Chesterfield up one place to sixth. They are on 167 points, 103 behind leaders Cutthorpe.
An outstanding all-round performance by Alex Fowkes guided Chesterfield Seconds to an 81-run win over Belper Amateurs in Division One North at Queen's Park.
Fowkes opened the innings and batted throughout the 45 overs. Watchful at first, he gradually accelerated and was 87 not out as Chesterfield made 213-8.
Bowling medium pace, he then took 5-36 to help dismiss the visitors for 132. Wrist-spinner Joel Hiron took 3-39.
Chesterfield's third team were all out for 140 in an eight-wicket defeat to Holmesfield Seconds in Division Eight.
On Saturday, Chesterfield host Ilkeston Rutland while the Seconds travel to Shipley Hall. The third team host Pilsley & Clay Cross Seconds at Deer Park, Wingerworth.