The 18-year old midfielder managed to volley home from the edge of the area in the 11th minute at Turf Moor before Charlie Austin levelled prior to the half-hour mark from the penalty spot.
Chalobah was substituted at half-time with manager Gianfranco Zola explaining the reasons for his game ending prematurely.
"He had a dead leg and had to come off," said the Hornets boss.
Chalobah's Watford teammate Alexandre Geijo was full of praise for the England youth international, suggesting he is good enough to play in the Premier League.
"He is definitely a player who can play in the Premier League," Geijo said.
"He has quality and he is just 17 (18). It is incredible. He has confidence, and no problem taking the ball and responsibility."