Wayne White (3-43) and Mark Footitt (3-74) claimed three wickets apiece to help give Derbyshire the edge after Day One against Surrey at The 3aaa County Ground.
Tom Taylor (2-30) and Wes Durston (2-31) were also amongst the wickets as Surrey lost their final four wickets for just four runs to be dismissed for 239 shortly after tea, despite Gary Wilson (65) and Gareth Batty (41) producing a stubborn partnership of 80.
Derbyshire had 21 overs to negotiate before stumps and they reached 64-1 with Hamish Rutherford (23*) making a solid start on his four-day debut for Derbyshire alongside opener Ben Slater (21*), meaning Derbyshire trail by 175 runs heading into the second day at Derby.
After losing the toss and being asked to bat first, Surrey saw off the new ball before White got the breakthrough for Derbyshire as Arun Harinath edged to wicketkeeper Tom Poynton, his first of four catches, for 35.
Taylor then had Zafar Ansari caught at second slip for 13 the following over, before clean bowling Dominic Sibley with a gem of a delivery when the batsman was on 10.
South Africa international Dean Elgar and former England Under 19s player Ben Foakes guided Surrey through to lunch on 90-3, but Foakes fell soon after as he went lbw for 15 off the bowling of Footitt.
Elgar played fluently for his 44 but he skied a Durston delivery to Tony Palladino who took a good catch at mid-off, before James Burke fell shortly after as he was stumped by Poynton for a single off the same bowler.
Captain Batty joined Wilson at the crease with Surrey on 155-6, but they shared a 80-run stand before White had Batty caught behind for 41, with the visitors on 235-7.
Surrey then lost three more wickets for just four runs to be dismissed for 239. Footitt had Tom Curran caught behind by Poynton without scoring, before White grabbed his third by trapping Wilson lbw for 65. Footitt then removed number eleven Tim Linley as Poynton took his fourth, as the left-arm quick returned figures of 3-74.
Derbyshire lost newly appointed Vice-Captain Billy Godleman early on in their reply, caught behind off the bowling of Luke Fletcher for 10.
But New Zealand international Rutherford and Slater guided Derbyshire through to the close on 64-1 with minimum fuss, trailing by 175 runs heading into Day Two.
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Derbyshire are back in home NatWest T20 Blast action on Friday 26 June when they welcome Notts Outlaws to The 3aaa County Ground for the eagerly-awaited East Midlands derby.