They staged something of a fightback but the hosts were emphatic five-wicket winners of the Division One clash.
Chesterfield had the disadvantage of being put in to bat in tricky conditions with light rain falling at intervals during their innings.
Even so, they well looked well placed at 85-2 in the 20th of their 50 overs.
Skipper Harry Wilmott, who got off the mark with a pull for six in the second over, was going strongly on 47 with good support from Luke Westwell (26). But then Wilmott was caught at third man and the innings went into freefall.
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The next 11 overs yielded only 15 runs as Chesterfield lost five more wickets. Seamer Dave Greaves (3-22) and spinner Saad Khattak (3-38) did most of the damage.
Saad Sarwary, batting at No. 10, launched a counter-attack, hitting out in typically enterprising fashion before he was last out, stumped off Khattak for 32.
Chesterfield made 147 and that total was soon put into perspective when Paul Holmes (29) and Alexander Eyre (66) launched the Morton reply with a stand of 95.
Five wickets fell in the later stages but the home side reached their target in the 28th over.
Chesterfield stay sixth in the 12-team table on 192 points, 106 behind leaders Cutthorpe.
Chesterfield Seconds lost to their Ilkeston Rutland counterparts by five wickets at Queen's Park in a Division Three North game reduced to 30 overs-a-side because of rain.
Put in, Chesterfield slipped to 47-6 in gloomy conditions despite a battling 35 from opener Alex Fowkes. As the skies brightened and batting became less fraught, Tim Kirk (24 not out) and Matt Grant (25) guided the hosts to 102-7.
But Josh Banks' 45 put Ilkeston on course for a win they sealed with five overs to spare.
The Sunday side lost by six wickets to Hucknall in the Premier Section of the Mansfield & District League after being bowled out for 160.
On Saturday Chesterfield travel to Clifton and the Seconds play Ashover Barbarians at Queen's Park. The Sunday team host Farnsfield.