Frost pulled into a share of the lead by carding a six-under 66 while Bryant and Eger both registered four-under 68s. All three ended the day with 36-hole totals of eight-under-par 136 in the Champions Tour event at Saucier, Miss.
Fourth place was held by Jay Haas at minus-six after he fired a 68, while Tom Kite also shot 68 to claim a share of fifth at five-under-par 139 along with Joey Sindelar, Tommy Armour III and Rod Spittle, all of whom shot 69s.
Frost, a 10-time PGA Tour winner, is seeking his first Champions win.
The South African claimed the lead at nine-under with a birdie on No. 13. But a bogey on the par-3 17th hole caused him to fall into the three-way tie.