Knocked out of the FA Cup by non-league Northwich on Sunday, Charlton missed out on a place in the last four of the Johnstone's Paint Trophy.
Thomas' goal was also his first in 44 matches for Southampton while Rickie Lambert added another for his 12th since joining Saints in August for £1million.
Substitute Leon McKenzie pulled a goal back for Charlton in the second minute of injury-time but Southampton held on to progress.
Thomas scored from six yards in the 34th minute and on-loan Michail Antonio struck the post five minutes later, and Southampton's second came in the 63rd minute when Adam Lallana created room for Lambert to crash home from the edge of the area.
McKenzie came on in the 68th minute and scored from close-range in stoppage-time after Luke Holden had found him at the near post with a cross.