Durham duly knocked off the runs to record a seven-wicket win in the 45 overs per side competition.
It was a spectacular way for Shoaib, nicknamed the 'Rawalpindi Express', to mark his return to County cricket after missing Durham's last two championship matches with a rib injury.
After Neil Killeen had dismissed opener Andrew Gait for a duck with the sixth ball, Shoaib continued Derbyshire's slump by taking two wickets in his fourth over.
First he had Chris Bassano caught behind by wicketkeeper Andrew Pratt for a duck before Hassan Adnan went the same way first ball.
In all five Derbyshire batsmen, including four of their top five, fell for nought.
Three of those ducks came against Shoaib who also had James Bryant caught by Nicky Peng for nought before collecting his fourth wicket when Graeme Welch (one) saw his miscued cut taken at third man.
Shoaib's onslaught saw Derbyshire collapse to 19 for six and only a last wicket stand of 41 between Luke Sutton (43) and West Indian Darren Powell (18 not out) got the visitors in sight of 100.
In the One-day league bowlers are allowed a maximum of nine overs and Shoaib returned the impressive analysis of nine overs, three maidens, 15 runs and four wickets.
Even more incredible, in some respects, was Killeen's haul of two wickets for five runs in 8.3 overs featuring seven maidens.
Meanwhile Mark Davies's nine overs cost just 10 runs.