Morgan Schneiderlin and Rickie Lambert fired Saints into a two-goal lead but Philippe Coutinho, a reported January target for the hosts, reduced the deficit in first-half stoppage time.
Brendan Rodgers' side pushed hard for a leveller but Rodriguez made sure of the three points with 10 minutes remaining, putting Saints seven points clear of the drop zone in front of a record Premier League crowd at St Mary's of 32,070.
- Sports & Recreation
- Philippe Coutinho
- Rickie Lambert