Before the final round on Sunday, Man City leads by one point ahead of Liverpool.
City host Aston Villa while Liverpool host Wolverhampton.
Coach Jürgen Klopp showed his biggest smile when he walked around the pitch with a close-up cameraman and hugged his players, a B-team line-up.
Southampton made a rush in the final minutes to get an equalizer but Liverpool held off and took the necessary victory.
The team also has six goals worse goal difference than City.
Liverpool got an early shock when Redmond gave Southampton the lead in the 13th minute with 1-0 but the team turned after goals from Minamino in the first half and Matip in the middle of the second half.