The Portugal international was tackled by Son Heung-min, who was sent off, before landing awkwardly and falling into Serge Aurier.
The South Korean was shown a straight red and was immediately reduced to tears after seeing the damage his challenge had caused the midfielder.
Tottenham and Everton players were left distressed by the incident as Gomes needed immediate medical attention.
He left the field on a stretcher to the applause of Goodison Park.
Several players began to panic when they caught a glimpse of his ankle, which was twisted 90 degrees to the right from its normal position.