Kuchar and Taylor tied in regulation at 17-under-par 271 Sunday and each parred the first two extra holes before play was suspended by darkness at the Atunyote Golf Club.
Taylor shot a 6-under 66 and Kuchar, who was third-round co-leader with Scott Piercy, had a 69 in the final round.
The playoff is to resume at 8:30 a.m. EDT Monday.
Tim Petrovic (67) and Leif Olson (69) tied for third place at 16-under 272. Jimmy Walker and John Senden (67) finished at 273.
Piercy slipped to a 1-over 73 and 275, tied for 12th place.