Grant Flower faced 43 balls without adding to his overnight score of five before becoming Rashid's first victim, with the leg-spinner also accounting for Phillips and last-man Andy Carter.
Lyth, the first man to reach 1,000 runs this season, and Rudolph gave the Division One leaders a solid start but their partnership was ended when Carter got one to climb on the South African to have him caught behind.
Left-hander Lyth looked set for his fourth century of the summer when he was bowled around his legs by paceman Chris Wright, his dismissal sandwiched between two strikes by left-arm spinner Phillips.
At 177-4, Gale combined with Gerard Brophy (25 not out) for a stand of 38, but was caught behind attempting to cut Tom Westley.
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