Goydos, 56, had an 8-under 136 total at TPC Sugarloaf. He has five senior victories after winning twice on the PGA Tour.
Andrade eagled the par-5 18th in a 68.
First-round leader Stephen Ames followed his opening 66 with a 72 to drop into a tie for third at 6 under with 2019 winner Scott McCarron (68), 2014 champion Miguel Angel Jimenez (68), Dicky Pride (67) and Kirk Triplett (68). McCarron also won two PGA Tour events at TPC Sugarloaf.
Hall of Fame pitcher John Smoltz bogeyed the final three holes for a 77. He opened with an 84 and was 76th among the 78 finishes at 17 over.