Jack Berrisford was an early casualty, caught by Tilly off Allen for 0, as Cropston won the toss in this Division One clash and put Barkby into bat.
Ian Kirk and Steve Flowers took the score to 61 before Hickenbottom bowled the former for 26.
Matt Harby joined Flowers, and with the score on 99, Hickenbottom had Flowers caught for 34.
Barkby lost the wickets of Drake, Ghorecha and Waplington while adding only 10 runs to their score, Harby with 28 and Troop 25, while an unbeaten 12 from James Kirk and eight not out from Jack Johnson took the visitors to 168-8 from their 45 overs.
Ian and James Kirk opened the bowling and soon had Cropston in trouble, taking the wickets of both openers with only five runs on the board.
With the score on 30, James Kirk had Finnemore caught by Flowers, and Townsend came into the attack and struck with his second ball, having Pollard well caught by Johnson with the score on 36.
A brilliant display of spin bowling from Townsend had the dangerous Rao caught brilliantly by Berrisford on his way to excellent figures of 6 for 17.
Young Jack Johnson also claimed his maiden First XI wicket for Barkby as the home side were dismissed for 103 in the 31st over.
Barkby achieved 30 points for their third victory of the season which keeps them within 40 points of the top two.
Barkby: Berrisford 0, I. Kirk 26, Flowers 34, Harby 28, Drake 0, Ghorecha 0, Waplington 4, Troop 25, J. Kirk 12*, Johnson 8*, Extras 31. Total: 168-8.
Bowling: I. Kirk 6-0-18-1; J. Kirk 6-1-16-2; Townsend 9.5-1-17-6; Waplington 4-0-32-0; Johnson 5-0-17-1.