Pate -- seeking his first Champions Tour victory -- and seven-time winner Funk each finished the day at 8-under-par 136.
Andrew Magee and Jay Don Blake, each carded a 2-under 70 to finish the day tied for third at 7-under.
Russ Cochran, who led after Friday's first round, tumbled into a ninth-place tie at 5-under following a round of 1-over 73 that featured a double-bogey on the 16th.
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