After a goalless first half at St Mary’s Stadium, Hudson-Odoi made the breakthrough on 56 minutes, a day after signing a new five-year deal.
The winger went off at 76 minutes as he sought to regain his fitness, by which time Chelsea had doubled their lead through Clinton Mola.
Mola was teed up by Reece James, who went off at the same time as Hudson-Odoi, having also recently returned from injury.
The win returned Chelsea to the top of the PL2 Division 1 table, on 14 points, two clear of Everton and Arsenal.
Southampton remain bottom on four points.