Eaks followed his Friday 61 with a 68 in the second round for a 15-under 129. The co-leaders are four strokes ahead of Gil Morgan, who had a 66 Saturday to hold third place.
Mark Wiebe (67) is fourth at 10-under 134. Tom McKnight (69) is in fifth place at 135.
Eaks is looking for his second win of the year and fourth on the Champions Tour. Jenkins has seven victories on the senior circuit, but none since 2006.
Mark McNulty (69), Gene Jones (68), Bruce Vaughan (70) and Tradition winner Fred Funk (71) are tied for sixth at 136.
Swim Week Miami Beach 2014 [PHOTOS]