The Brazilian forward struck with just over 15 minutes remaining, reacting quickest to convert Pape Matar Sarr’s clever backheel and briefly give Spurs hope of a comeback after trailing 2-0.
Although the milestone was significant, the visitors could not find an equaliser in the closing stages.
Spurs became only the sixth club to reach 2,000 Premier League goals since the competition began in 1992.
Their first came through Gordon Durie in a 2-2 draw against Crystal Palace in August 1992, while Les Ferdinand, Jermain Defoe and Juan Foyth scored the landmark 500th, 1,000th and 1,500th goals respectively.
Richarlison’s strike also continued his strong individual season as the goal took him to 12 in all competitions, including 11 in the Premier League, matching his best scoring return for Tottenham.
Overall, he now has 75 Premier League goals in his career.