Mount scored the second goal at St Mary’s, taking his personal tally to four Premier League goals this season.
Fellow youngster Tammy Abraham also scored before N’Golo Kante and Michy Batshuayi made the game safe, while there was also a first start of the season for Callum Hudson-Odoi after his return from injury.
The Southampton result made it four wins in a row in all competitions for the Blues, and Mount thinks the influence of manager Frank Lampard has been vital.
"It's very important,” he told BBC Sport.
“It's the whole squad - there's so much competition and you always have to stay on top of your game. The manager makes us work and try to do your best to get into the team.
"It's a transitional team but we don't have that in our heads, we want to get as high in the table as we can.
“A lot of the young boys around us have played together for a long time, it's good having these boys around you in the senior team - it's a massive achievement and now we're looking forward to international break."
While things didn’t immediately click into gear at the start of Lampard’s tenure, Chelsea go into the international break fifth in the table and with a first Champions League win under their belts.
Sunday’s results mean they are only two points behind champions Manchester City and, while leaders Liverpool are ten points ahead, Mount has been thrilled with his and his side’s progress in the opening months of the season.
"It's been going good away from home,” he added. “There are little things we can work on, obviously conceding, and we had a tough period but away from home we've been very good.
"You've always got to have that confidence in yourself. To be fair, I probably didn't think it would go this well at the start. Everyone is working hard, you can see how much it means to us."