Glamorgan went into the game after a convincing 65 run victory at Gloucestershire, while Derbyshire also recorded a win over Sussex by six wickets.
There were two changes for both sides as Bethan Ellis and Amy Wheeler were drafted in for Glamorgan, while Prisha Bedi and Francesca Clarke stepped in for the visitors.
On a scorching afternoon at Sophia Gardens, Jeanes produced another dominant display as she and Bethan Ellis helped Glamorgan race to 60-1 after the powerplay.
Jeanes smashed 14 boundaries and helped Glamorgan survive a mid-innings wobble where four wickets fell for eight runs, two of them to Prisha Bedi.
Derbyshire finally dismissed her in the final over as she pulled high to mid wicket to mark the first of a hat-trick by the all rounder Knowling-Davies.
Georgia Parfitt and Charlotte Lambert also fell to the impressive Knowling-Davies leaving Gemma Porter 21 not out as Glamorgan left Derbyshire a reasonable target of 168 to win.
Despite 14 runs in what was a promising first over, Derbyshire slumped to just 41-4 in the powerplay as the away side could not get going with the bat.
Cobb produced a fine display of bowling as she took three wickets for just 10 runs as the home side turned the screw in the second innings.
In an anti-climactic ending, Derbyshire captain Adrianna Davies was unable to bat due to injury as they slumped to 75 all out after 14.3 overs.
Glamorgan’s Daisy Jeanes told BBC Sport Wales: “We set ourselves up with a really good total to defend with the ball.
“We try to go hard from the beginning and use the hard ball in the powerplay, then it was looking to rotate (strike) more as the ball goes soft.
“It feels good (to make a career best), a good day out and we’re so happy, we’ll just enjoy the wins as they come.
“Individual performances help towards professional contracts, but for now we’re trying to win as a team.”