Crystal Palace's Pino was forced to play out the final few minutes, struggling with a shoulder injury after Luis de la Fuente had used his three windows to make substitutions.
Williams was only introduced 15 minutes from time after being nursed back into action after an injury-disrupted season at Athletic Bilbao.
But he ended the game with an issue that could be a body blow to La Roja's hopes of World Cup glory.
The latest injuries leave De la Fuente desperately short of options in wide areas.
Lamine Yamal is yet to play 90 minutes in over two months on his return from a hamstring injury and Liverpool's new signing Victor Munoz has not featured at the World Cup after a setback in his return from a muscle problem.
"Nico was experiencing some slight discomfort. It could be a strain or just fatigue; we’ll have to wait until tomorrow to know for sure," said De la Fuente.
"However, and I am really sad about this, what really concerns me is Yeremy's injury. It looks bad and there is a very strong possibility he will miss the rest of the tournament."
Spain were far from their fluid best in Guadalajara as Alex Baena's goal, thanks to a goalkeeping error from Fernando Muslera, secured top spot in Group H.
The European champions will next face Austria or Algeria in Los Angeles.
De la Fuente conceded his side must improve once the knockout stages get underway, but praised Spain's discipline as Uruguay lost their heads in bowing out of the tournament.
Some lenient refereeing from American official Ismail Elfath had allowed the South Americans' physical approach to thrive until Agustin Canobbio was shown a red card in stoppage time for a wild lunge on Pau Cubarsi.
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"I am proud of my players in a match that pushed us to the limit in every sense of the word, physically very demanding and rough, that we stood up to be counted," added De la Fuente.
"We know we can find ourselves in games like this and the most important thing is that we rose to the occasion, even if the performance wasn't particularly dazzling.
"In football, you can't always play with the brilliance you wish for, or that we are capable of showing at other times.
"We maintained an incredibly high level of concentration, responsibility, and composure, and we avoided rising to the many provocations that could have led to serious trouble."