Maggert, seeking his fourth PGA Tour title but first since 2006, matched Every at 12-under-par 198 after 54 holes.
Second-round leader Every posted a 2-under 68 at Waialae Country Club.
The pair finished two shots ahead of three players.
Knotted in sixth at 9-under 201 were Duffy Waldorf (66) and D.A. Points (64).
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