The top-ranked Nadal didn't drop a set in three group-stage singles matches in Perth in the new international team competition, but was unable to break down a free-swinging Goffin in Sydney.
The winner of the doubles match will advance to the semi-finals against Australia.
Roberto Bautista Agut had given Spain a 1-0 lead when he continued his run of straight-set wins a 6-1, 6-4 victory over Kimmer Coppejans, a late replacement for Belgium playing captain Steve Darcis.
Nadal went into the second singles match as the favourite. The 11th-ranked David Goffin took it to Nadal, attacking at every opportunity and shutting down his rival's options. He got a break in the fifth game on a rare double-fault from the Spaniard. Nadal broke back immediately and then had five break points in the eighth game but couldn't convert any.
Goffin had four break points in the ninth game and eventually converted, then served out the set.
The second set lasted 82 minutes and contained two service breaks, with Goffin under intense pressure serving second to stay in the set.
Just as Nadal appeared to be getting on top, though, Goffin rallied and dominated the tiebreaker, clinching it with an ace on his second match point.