The trip to St Mary's was the German's 146th league match in charge of the Reds since taking over in October 2015.
The three points claimed after goals from Sadio Mane and Roberto Firmino helped Klopp surpass the mark previously set by Sir Kenny Dalglish, who reached the threshold in 150 fixtures.
Club statistician Ged Rea has broken down the numbers based on three points for a win.
Number of games to reach 300 league points
Jürgen Klopp – 146 (17/8/19)
Kenny Dalglish (first spell) – 150 (14/3/89)
Rafael Benitez – 159 (5/10/08)
Bob Paisley – 161 (8/4/78)
Bill Shankly – 166 (30/11/63)
Gerard Houllier – 169 (8/3/03)
Tom Watson – 197 (6/9/02)
Matt McQueen – 205 (2/1/28)
George Kay – 212 (25/8/48)
George Patterson – 220 (27/12/32)