Spurs forward Son, who set up Dele Alli to score the opening goal of the game at Goodison Park, was sent off after catching Gomes with a sliding challenge as the midfielder led a break over the halfway line.
Gomes then seemed to collide with Serge Aurier while off-balance and went to ground with what looked to be a significant injury to his right leg.
Players from both teams were left visibly distressed as medical staff attended to Gomes near the touchline.
A round of applause for Andre Gomes who gets carted off after suffering a horrific ankle injury.— NBC Sports Soccer (@NBCSportsSoccer) November 3, 2019
Wishing him all the best. pic.twitter.com/dCAk3rn8p3
Referee Martin Atkinson then showed a red card to Son, who looked distraught as he was helped away and down the tunnel.
After a long delay, Gomes was taken off on a stretcher to a standing ovation from all corners of the stadium, with Gylfi Sigurdsson coming on as his replacement.
There were 12 minutes of additional time at the end of the second half, following Gomes' injury and two length pauses for VAR reviews of possible penalties, neither of which resulted in spot-kicks being given.