Jacques Rudolph and night watchman Timm Van Der Gugten had put on 49, before Van Der Gugten was LBW in Palladino’s second over.
In his next over, Rudolph played an expansive drive, but edged to slip after scoring 32, and the Derbyshire seamer took his third wicket, when Owen Morgan, in his first game of the season, was LBW without scoring.
Nick Selman was fortunate to survive, when he was dropped by wicketkeeper Daryn Smit on seven, but Colin Ingram was soon into his stride with three fours through the offside.
Palladino was rested with figures of 8-3-18-3, but when Jeevan Mendis was given an over before the break, he had Ingram caught at slip for 18. At the tea interval, Glamorgan were 87-4, with Selman 12 and Aneurin Donald yet to score.