Both players finished 72 holes in regulation at 13-under 275.
In the final round, Romero shot 7-under 65 and Nielsen shot 2-under 70, with a birdie at the 18th and final hole to force the playoff.
It was Romero's first Champions Tour win.
Andy Bean was eighth at 8-under 280, and five players were one stroke further back at 7-under 281.
Loren Roberts, the 2005 champion, ballooned to a 4-over 76 Sunday and tied for 14th at 6-under 282.