The Blues' five-game winning run under Tuchel came to an end at St Mary's Stadium, with Mason Mount's second-half penalty enough only for a point after Takumi Minamino's good finish.
Southampton, who were on a six-game losing run in the league, had just 29 per cent of the ball and one shot on target.
However, they defended resolutely against a Chelsea side who failed to hit the target in the second half after Mount's 54th-minute equaliser.
Hudson-Odoi was brought on at half-time for Tammy Abraham but was himself substituted for Hakim Ziyech after a little over half an hour in which he failed to have a shot or create a chance, completed only seven passes and did not once win back possession for his side.