Hamish Rutherford scored his maiden half-century for the county, but it was Surrey who fought back on Day Two at The 3aaa County Ground.
Rutherford made a classy 59 but Derbyshire lost wickets at crucial times before Tony Palladino (35 not out) provided a late cameo to guide the hosts to a total of 207; a deficit of 32 runs.
Mark Footitt (2-40) bowled both Surrey openers in the evening session, before bad light ended the day’s play with the visitors on 77-2, a lead of 109 runs.
Derbyshire began Day Two on 64-1, with Rutherford and Ben Slater surviving a tricky half hour in overcast conditions.
Luke Fletcher, on loan from Nottinghamshire, began to work his magic as Slater (28) and Madsen (4) fell in quick succession with both batsmen caught behind by Gary Wilson. Chesney Hughes was then trapped lbw by Fletcher without scoring, with the bowler claiming his fourth wicket of the innings to reduce Derbyshire to 110-4.
Rutherford brought his half-century up from 100 balls on his LV= County Championship debut for the county, but he was out soon after as he edged to first slip off the bowling of Tom Curran for 59.
Two more quick wickets fell, but Wes Durston remained firm and played well for his 33 before he was caught behind off Tim Linley, with James Burke then having Tom Taylor caught by Dean Elgar for just three as the hosts were reduced to 177-9.
Palladino played aggressively whilst batting with number 11 Footitt to earn Derbyshire a batting point, before Footitt was caught behind off Curran for two and Derbyshire were all out for 207.
Surrey began their second innings with a lead of 32 runs, but lost opener Arun Harinath early on for six, with Footitt removing the batsman’s off-stump.
Footitt then bowled the other opening batsman, Zafar Ansari, for 19 before a number of delays due to rain and bad light halted Derbyshire’s momentum and Surrey closed on 77-2 with a lead of 109 runs.
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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.