A mistake from Michael Essien gifted Jay Rodriguez an opening goal after only 13 seconds at Stamford Bridge, but the hosts produced a second-half fightback to secure a victory which cut that gap to Premier League leaders Arsenal to four points.
Gary Cahill equalised 10 minutes after the break and John Terry put second-placed Chelsea in front seven minutes later in his 400th Premier League appearance for the London club.
Demba Ba sealed the points after 89 minutes and Mourinho was delighted with the manner in which his side responded to the early goal and the midweek UEFA Champions League defeat at Basel.
The former Real Madrid manager told Sky Sports: "It was the worst possible start and we had to wait for the second half to come back into the game.
"In the second half we played 4-4-2 and gave Southampton what they didn't expect. Mata gave us what we needed, he was playing as a fake winger and we gave Southampton problems that they could not solve.
"Southampton like to play from the back but by us playing two strikers pressing, it didn't allow that.
"We showed character, emotion and heart. I think there was a bit of everything (in the second half).
"I told the players at half-time it's easy to play well when you're winning and crowd is supporting you, but I think it is more enjoyable when it's more difficult. I think it was a very deserved result."
Mourinho also defended Essien after the midfielder endured a miserable afternoon in which he was at fault for Rodriguez's goal before being booked for diving and substituted at half-time in his first Premier League start since May 2012.
The Portuguese said: "Everybody makes mistakes and Essien was trying to play when he made his, but he also played his part in our stability."
