Nadal, who has been dealing with tendinitis in his right knee, rallied before dropping a 7-6 (5), 6-7 (4), 6-4 decision to Goffin.
"I'm not ready to play," Nadal said after the match. "I fought a lot knowing it was my last match of the season. But my commitment was to try. I've missed this event too many times in my career."
Countryman Pablo Carreno Busta, an alternate, will take the place of Nadal, who admitted prior to the tournament that his knee was "not perfect." The injury also forced Nadal to withdraw from the Paris Masters earlier this month.
Still, Nadal showed his mettle against the Belgian, saving four match points to push the contest to a decisive third set.
"I don't know how I picked myself up after losing the four match points," Goffin said. "I had no regrets and I just wanted to keep going and try to enjoy every point."
The Spaniard saved eight of 13 break points but Goffin finally put Nadal away with an ace -- his 14th of the match -- to claim his first victory over a No. 1-ranked opponent.
"It was a tough fight until the end. Rafa is one of the strongest players mentally on the tour," Goffin said after the two-hour, 36-minute match. "I am so happy to finally find the key to win this match. It is so special to do it here.
Thiem double-faulted twice in the 11th game of the decisive set against Bulgarian, who then closed out the match on his serve. Dimitrov broke Thiem three times.
"It, for me, was just one of those new experiences that I think I'm going to remember for the rest of my life, I think appreciate for the rest of my life," Dimitrov said. "This is where I always wanted to be at, among the top players, also being able to come through in my first match, it's only positive."