Duanne Olivier claimed 3-51 before rain halted Derbyshire’s progress and Durham closed on 155-6, leading by 46 runs.
The tall South Africa quick struck in quick succession after lunch to leave Derbyshire in a strong position after Tom Latham had earlier hit 67.
Heavy rain fell at tea forcing play to be abandoned with the hosts on 155-6, leading by 46 runs with Gareth Harte unbeaten on 24 and Cameron Steel not out on six.
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